The Rambam, in his introduction to the Mishna (and Oral Law in general) explains that the definitions of the Mitzvos were passed down from Moshe Rabbeinu, and there are no arguments on these. In this category is our interpretation of the פרי עץ הדר as the Esrog, that Shechita means the slaughter as we know it, that מלאכה on Shabbos means the 39 tasks, and the many details of the Succah.
There are also many issues and scenarios that came up after Moshe Rabbeinu, and it is impossible to fit any and all scenarios into any book or scroll. But Moshe gave us the tools to deal with these. There are thirteen methods of extrapolation that were passed down and we used these methods to deal with the new questions that arose over time. Since these are derived by us there will be differences of opinion of what exactly to learn from the verses. The differences are minute since the methods we use are the same. But it is unavoidable to have slightly different outcomes depending on different perspectives.
The Rambam explains that in early times, when the students spent much time with their rabbis, they would even pick up their attitude and perspective to the extent that there would be no argument among the students when tackling new issues. They would all view it the same, with the perspective that was passed on to them.
Although we have these differences of opinion, the Talmud in Chagiga (3b) tells us:
Should a man say: How in these circumstances shall I learn Torah? Therefore the text says: ‘All of them are given from one Shepherd’. One God gave them; one leader uttered them from the mouth of the Lord of all creation, blessed be He; for it is written: (Exodus 20:1) ‘And God spoke all these words’.
The Tanna DeBei Eliyahu (c. 2) likens the relationship of Oral Law and Written Law to a case of a king who gave his servants wheat along with bundles of flax. Those who were smart made fine table cloths from the flax and loaves of bread with the wheat and welcomed the king proudly when he came to check up on them.
The same goes for the Torah. We were given the original laws and the rules by which to extrapolate their details and application. With these we produce many volumes of law and thought, all directly based on what we learned and received. There is no outside input. We aren't introducing any ideas outside the framework of the tools which were passed down.
To sum this all up, Oral Law includes those laws which are directly passed down, and those laws which were derived using the tools which were passed down.
Another category is the rabbinic law. These are the rulings of Gezeiros, or boundaries, in which the rabbis decreed certain things in order to round out the biblical laws. This means that at times something might be technically permitted but to the untrained eye it seems no different from what is actually prohibited. In these cases the rabbis outlawed the likeness of the biblical prohibition. Other rabbinic prohibitions are to keep people away from scenarios that would have them easily sin with or without noticing.
These too are actually fulfilling the tradition and are based on their understanding of a situation and what they learned about the role of leaders in enforcing the Torah and making it accessible to all.
Along these lines, the early Great Assembly, the Anshei Knesses Hagedolah, codified and formulated the format of the prayers. Prayer itself is a biblical requirement but its format and timing is rabbinic. But this is all part of Oral Law.