I know that circumcision was existent in various nations before and after Matan Torah, and it was and still is practiced with or without the Torah.
What's the difference between a Jewish circumcision and a secular one, and how did Tzipporah know how to perform it and what to cut, given that the Oral Torah wasn't given yet?
Tziporrah knew how to do it simply by watching it being done by her older son. The Jews circumcised their sons since the time of Abraham.
Based on the comments I am going to go out on a limb and guess the question is how a woman (Tzipporah) could of done the bris for Moshe's son, if she is a woman and cannot be a mohel (according to some in the Gemara). Based on this, the question is if it is possible that her bris was different than nowadays, since it was before Matan Torah. If I am mistaken please advise.
The Gemara in Avoda Zara 27a asks this very question
The Gemara raises a difficulty against this explanation: And is there anyone who says that a woman may not perform circumcision? But isn’t it written: “Then Zipporah took [vattikkaḥ] a flint and cut off the foreskin of her son” (Exodus 4:25). This verse explicitly states that a circumcision was performed by a woman. The Gemara answers that one should read into the verse: And she caused to be taken [vattakkaḥ], i.e., she did not take a flint herself. But isn’t it written: And she cut off [vattikhrot]? Read into the verse: And she caused to be cut off [vattakhret], as she told another person to take a flint and cut off her son’s foreskin, and he did so. The Gemara provides an alternative explanation: And if you wish, say instead: She came and began the act, and Moses came and completed the circumcision
Indeed it's possible that Tzipporah did only the first step of the milah, the cutting of the foreskin, and not the second, peeling back the membrane (periah). The Talmud (Yevamot 71b) states that the latter step was not part of the original commandment given to Abraham. The first record we have of it being obligatory, according to that opinion, is when Joshua performed a mass circumcision of the Jewish males upon their entry into the Land of Israel (Joshua 5:2; the Talmud understands the word שנית ("a second time") in that verse to mean a second step of the circumcision).
Now, some of the commentaries there (Tosafot, Ramban, et al) argue that periah might have been performed earlier too, just that it wasn't required. But not necessarily does that mean that Tzipporah would have done so.
I'm not sure if non-Jewish sources would be allowed but it was quite a common practice in ancient Egypt [500 years before Abraham] so it would not be impossible for her to know based on general knowledge.
From History_of_circumcision:
Sixth Dynasty (2345–2181 BCE) tomb artwork in Egypt has been thought to be the oldest documentary evidence of circumcision, the most ancient depiction being a bas-relief from the necropolis at Saqqara (c. 2400 BCE) with the inscriptions reading: "The ointment is to make it acceptable." and "Hold him so that he does not fall".[citation needed] In the oldest written account, by an Egyptian named Uha, in the 23rd century BCE, he describes a mass circumcision and boasts of his ability to stoically endure the pain: "When I was circumcised, together with one hundred and twenty men ... there was none thereof who hit out, there was none thereof who was hit, and there was none thereof who scratched and there was none thereof who was scratched."
