Is there any difference If I just say "you saw me study"?
Answer from a Native speaker
No, you're right! You can use "you saw me study" here. "Saw" (which is past tense for "to see") has been used here, so we can infer that the speaker is talking about an action that occurred in the past. If the speaker said "you saw me study," it would imply that the action was completed and closed In the past. Meanwhile, "you saw me studying" is in the past progressive tense, which means that the speaker's friend saw them studying and the action continued to happen, but they didn't necessarily see it end. So you can think of the difference as being that while both "study" and "studying" are attached to "saw," indicating an action in the past, the first indicates that the action of studying was witnessed and that it ended, and the second indicates that the action was witnessed but did not necessarily end. Although these two are ultimately different tenses, in everyday conversation people do not differentiate between the two. For the most part, you can use either in situations like this one. Ex: The last time I saw you exercising, you were struggling a lot more. (action was witnessed, did not necessarily end) Ex: The last time I saw you exercise, you were struggling a lot more. (action was witnessed, and ended)