Top is pretty self explanatory. Hot takes a combination of how many votes they got and how recent they are. And I think active is based on the number of new comments, although I'm not entirely sure.
pretty sure this is generally correct just from using them. Though i will say, active seems to keep the same posts on it for a long time. like weeks it seems. idk why
There also seems to be an issue with very old posts showing up in sorting algorithms where they don't belong, like 2 year old posts on the first page of Hot results.