It depends on the program, and even more so, the student and the mentor. It can also vary over time, with more direction early on in a graduate program, and less direction later. Some mentors are very directive, and basically treat students as labor executing tasks they don't have time or want to do. Other times, the student is coming up with all the ideas and the mentor is facilitating it with resources or even nothing but uncertain advice or permissions now and then.

This can lead to a lot of problems as I think in some fields, by some academics, the default assumption is the former, when it's really the latter. This leads to a kind of overattribution of contribution by senior faculty, or conversely, an underappreciation of less senior individuals. The tendency for senior faculty be listed last on papers, and therefore, for the first and last authors to accumulate credit, is a good example of how twisted this logic has become.

It's one tiny example of enormous problems with credit in academics (but also maybe far afield from your question).