This might be a very silly question, but I'm just trying to make sure I'm going about things for my senior project right. Does the Google Drive API connect to the user's personal Drive space?
Actually it's a very good question because it confuses a lot of first time Drive users.
The answer is, It depends.
There are two distinct Google Drive APIs, with different characteristics and capabilities. These are the Google Drive REST API and the Google Drive Android API (GDAA). You have tagged your question with both.
The Google Drive REST API can connect to any Drive account, e.g. your own, one of your users, or a Service Account. Which account it connects to is determined by how the Access Token was generated.
The GDAA only connects to the Google account associated with the Android device it's running on.