Personally, the biggest difference to me is that academic theatre is supposed to prepare you for professional theatre, but sometimes it doesn't. Academic theatre is not as regulated as far as rules and guidelines, at least in my experience. There is also the key difference that academic theatre is limited to students who also have work, classes, and other things. Therefore, the rehearsal schedules are very different. Although there are rules in both academic and professional theatre about when you can rehearse, they are different. Some professional companies rehearse 8 hour days, in 1 1/2 hour blocks with breaks; others do not. I have worked in professional companies where the rehearsal schedules are the same as academic theatre, so it all just depends. In academic theatre, you can usually only rehearse at night for a few hours and then maybe weekends depending on what school you go to.
Union plays a large role in these differences, because there are things that Stage Managers are expected to do in professional settings that academic theatre bypasses. I also think that sometimes the Stage Manager is taken less seriously in academic theatre, which is frustrating. You are working with your peers - some do not even know what a Stage Manager is until you explain the job - and sometimes it is difficult to do your job when people are not really taking you seriously. In professional theatre, more people know the responsibilities and jobs of a Stage Manager and know how large their contribution is to the production. I was definitely more appreciated in my first professional job than in any of my academic experiences, and it was quite startling to me how much people really respected me and my job.
I think another key difference is that in academic theatre, you are mostly working with teachers/professors who are directing, which could make some people quite nervous. As a Stage Manager, you don't want to overstep your bounds, especially if the director is also one of your professors and you are worried about your grade in their class or what they say about you in general, etc. In professional theatre, sometimes you don't even know the director or musical director, and although that can make some people nervous or uncomfortable, sometimes it can also make you quite confident. I think that having a professor as a director can be quite nervewracking, and it is a huge difference between academic and professional theatre.
I would recommend that you get a copy of the Equity handbook and read the responsibilities of a Stage Manager, and then compare/contrast it to your experience in academic theatre. ( I am assuming here that you are a Stage Manager and are SMing in an academic setting.) I think that everyone's situation in academic or professional theatre is going to vary, so you are probably going to get a variety of different answers. These are just some of the things that I've noticed in my experience, so I hope it helps. Best of Luck on your paper