I was asked this question by a friend of mine and at first I thought it was so simple (and maybe it is, maybe I just don’t have enough Torah knowledge to know the answer) but when I tried to explain the difference, I kept getting caught by my friend saying, that’s the same thing as a rov/chazakah. They are both halachically accepted forms of assumptions based on the probability that a certain outcome will repeat itself.
There are many types of chazakos and rovs, so it's good to define our terms before we compare them. What both of them have in common is they tend to address sefeikos, or uncertainties.
Chazaka D'MeIkara חזקה דמעיקרא
Basically, assume what was, will be. For example: חזקת כשרות, חזקת פנויה, חזקת אשת איש, חזקת איסור, or in English: something is still kosher, someone is still single, someone is still married, something is still forbidden. Even if you see that something has changed, you assume it changed at the last possible moment. While assuming things don't change could be logical (status quo), this latter novelty is not logical. It is a decree of the writ, a גזרת הכתוב. See Chullin 10b for the source and discussion on this type of chazaka.
Chezkas HaGuf חזקת הגוף
Similar to חזקה דמעיקרא, basically put it's the assumption that something physical hasn't changed. See Kesubos 12b for an example. Some say that this is stronger that a typical חזקה דמעיקרא (see Shev Shemaatesa 1:15).
Chezkas Mammon חזקת ממון
The gemarra (Bava Kamma 46b) calls this logical, to the point that you don't even need a source for it. Essentially it's the assumption that your possessions are yours until proven otherwise.
Behavioral Chazakos חזקה אדם וגו'
This is the assumption that people usually act a certain way. For example חזקה אין אדם עושה סעודה ומפסידה, we assume a person won't make a wedding feast only to ruin his marriage the next day (Kesubos 10a). חזקה אין אשה מעיזה פניה בפני בעלה, a woman wouldn't brazenly lie in front of her husband that he divorced her (Gittin 64b). More on this below.
Chezkas Gimmel Pa'amim חזקת ג' פעמים
We assume something that happened three times will continue to happen (שור המועד (Exodus 21:29), קטלנית (Yevamos 64b)).
Soklin al HaChazakos סוקלין על החזקות
Something that we assumed was true due to some proof (a single witness (see Mishneh Torah Hilchos Sanhedrin 16:6), logic), we will use even to execute punishments. For example, a new couple comes to town with two children. They act as a family, so we assume they're all related. If they commit incest together, they are punished based off that chazaka (Kiddushin 80a).
The gemarra in Chullin 11a teaches that there are two types of rov:
Ruba DeIsa Kaman רובא דאיתא קמן
A rov where the majority is before us. The classic example is 9 stores in town sell kosher meat and one sells non-kosher, and you find a piece of meat. Rov tells you to assume this piece of meat came from the majority.
Ruba DeLeisa Kaman רובא דליתא קמן
A rov where the majority isn't before us. There are different ways to define this. One way is this rov isn't known with cold-hard facts, it's just something that is generally known to be true (see Kovetz Shiurim I Bava Basra § 83, see there further for other explanations). For example, most animals are not born with a life-threatening blemish or illness. Or most people are not born infertile.
There are also different applications of rov. The above are referred to as Heilach achar HaRov, following the majority. Another application is Bittul BeRov, where in a mixture the minority becomes nullified and is considered like the majority.
Now, coming back to your question. I'm not sure which chazakos and rovs you and your friend were discussing, but my assumption is Behavioral Chazakos and Ruba DeLeisa Kaman. These work very similarly, since another way to phrase "there's a chazaka that a person would/not do X" as "most people do/don't do X". As noted by @JoelK, there are those that explicitly equate the two. Rav Asher Weiss in Minchas Asher Vayikra § 25 provides a proof that this is true. Chullin 11b suggests a source for Ruba DeLeisa Kaman is the fact that someone who bruises their father is sentenced to death, even though it's not known for sure who their father is. Rather, it's because rov beilos achar haba'al, even if the mother was unfaithful, most of the time she is with her husband. We therefore assume she became pregnant from him. The gemarra calls this a rov, yet the Yerushalmi Kiddushin 4:10 explains this case is the source for chazaka. Seemingly it's referring to Behavioral Chazakos, and thus the terms chazaka and rov in this context are interchangeable. See also Kiddushin 80a, which seems to call a rov a chazaka at the same time.
Not so other chazakos and rovs. You're right they both are assumptions that solve uncertainties, but they work differently, and they have different rules and laws. Some want to say that a Chazaka D'MeIkara doesn't answer the question, just tells you how to act, while Rov answers your uncertainty (see here for some sources). There's a rule that rov is stronger than certain chazakos (Niddah 18a), yet rov doesn't beat Chezkas Mammon (Bava Kamma 27b). They're not interchangeable or equatable. As well, clearly Bittul BeRov is different than chazakos.
There are indeed opinions which essentially understand certain forms of chazakah as a rov.
For example, R. Yisrael Isserlein writes in Terumat HaDeshen 207:
חזקה שאינה פוסקת שהיא באה מכח הרוב כמו החזקה אין עדים חתומים על השטר אא"כ נעשה גדול וכן חזקה אין אדם פורע בגו זמנו וחזקה שאין אדם עושה בעילת בעילת זנות דכל הני חזקות באים מן הרוב כלומר רוב בני אדם אין עושים אלא בענין זה אפילו בדיני נפשות סמכינן אחזקה כה"ג
A chazakah which does not cease, which comes from the power of rov, such as the chazakah that witnesses do not sign a document if they are underage, or the chazakah that a person does not repay a debt early, or the chazakah that a person will not make his act of sexual intercourse into an improper one, all these chazakot come from the power of rov i.e. most people only act in this way. We rely on such a chazakah even in capital cases.
R. Shimon Shkop in Sha'arei Yosher 3:3 distinguishes between a chazakah solely based on statistics (such as the chazakah that a woman will not falsely claim to her husband's face that he has divorced her) and a chazakah that is based on both statistics and a certain internal logic (such as the chazakah that people do not repay debts early).
He understands, based on the principle of ein holchin bemamon achar harov, that the former kind of chazakah cannot be used to extract money from a defendant, suggesting that this kind of chazakah is indistinguishable from rov. However, the latter kind of chazakah is strong enough to extract money; a chazakah based on logic as well as statistics is stronger than one based on statistics alone.
Another way to look at these types of chazakot in a way that is different from rov, is to understand them as discussing the way we perceive the world, rather than performing a statistical analysis.
For instance, R. Moshe Sofer in his Responsa Chatam Sofer Choshen Mishpat 67 writes of the chazakah that a debt is not repaid early that it is 'as if we are witnesses' (anan sahadi) that such is the case, and that such a chazakah can therefore be used to extract money. Similarly, R. Aryeh Leib HaKohen Heller in Shev Shmat'ta 6:22 writes that this chazakah is based on logic (sevara) and is thus stronger than rov.
The way I understand their approaches (although I grant that this is not necessarily the only way to read them) is that a chazakah, while it might be ultimately be based on a statistical phenomenon, takes on a life of its own when (for whatever reason) it becomes a feature of how people view the world. This is in distinction to a pure rov (such as the majority of animals do not have a fatal illness) where we are not coming in with any prior assumptions, and it is the questions that are asked which require us to perform a statistical analysis in order to come up with an answer.
I'm not going to go through the whole topic right now, and whatever I can say will be in contention. Rov is separated into 2 separate categories, one of which is based upon a פסוק in the Torah, אחרי הרבים להטות. This rov is called רובא דאיתא קמן and is based upon the majority of the current possibilities before us. What is considered 'before us' is a subject of debate. This is not a logical statistical conclusion. The רש"ש on בבא בתרא (צג:) brings down an argument in the פוסקים if in the classical case of תשעה חנויות (9 stores sells kosher and one sells non-kosher) what if the one large non-kosher store sells more meat per day than the other 9 kosher stores. Do we go based upon the number of stores or the volume of meat. This is a seemingly obvious question, as statistically the volume of meat is what determines the probability. But the question is if רובא דאיתא קמן looks at the amount of meat or the number of stores. This is to prove that רובא דליתא קמן is not statistics. חזקה, as Robev explained earlier, is not one thing. There are many different types of חזקות, the most common of which is חזקה דמעיקרא. This is also based upon a פסוק and is not statistical. An example is if I have two knives, one of which is kosher for שחיטה and one of which is not, and I grab one of them and use it to perform שחיטה. Afterwards I realize that I don't know which knife I use. חזקה makes the cow not kosher. This is again illogical, as there is nothing that says that since the cow was not kosher before, therefore I picked up knife a instead of knife b. This type of חזקה is called a הנהגה, a halachik tool that says when in doubt pick me. רובא דאיתא קמן is the most statistical of the bunch. It says that being that most people do x, or nature dictates y, they are more likely to be true. This type of rov is called a בירור by some, and actually establishes how we should look at the reality, not just a when in doubt do... sort of thing. I wrote a paper on this a while back if you're interested.
The terms can be used in slightly different ways (much as in the same way that the definition of "fact" changes when you compare it to "fiction" or "opinion") but one way to understand it is as follows:
A Chazaka has more depth because it inherently requires more "time" depth, more data points, to draw a conclusion.
The dice has four red sides and two green sides. If we don't remember the roll, we presume a red came up.
After 100 throws, the dice came up red 66 times. We presume the dice has four red sides and two green sides and then presume that an an additional unrecorded roll was red.
Both are usually associated with assumptions and clarifications in areas we lack certainty . The difference between them is what the assumption is based on.
Rov means majority. The assumption is being based on the statistical likelihood.
Additionally, a Rov/majority can influence the status of the minority in Halacha. For example, if a small amount of non-kosher food falls into a large amount of kosher the rov/majority of koshr food can make everything koher (ask your LOR before relying on this in a practical case)
Chazaka is simply an assumption. Based on the information we have and the way the world works we can assume something. It usually upholds the status quo until we have more information
A Rov is a stronger type of assumption than Chazaka and if they are contradicting each other the Rov would usually override the Chazaka