Depends on what product you are asking about. For Adobe Connect, there is not a teacher/student edition, so users of Adobe Connect all have access to the same program. However for other desktop (Creative Cloud) products, it tends to be around the EULA (End User Licensing Agreement) that states that you are not able to use a Teacher/Student edition for profit. But if you let us know what product you are asking about, we can move this to appropriate forum.
Just adding to above there is no difference in the application usage and its functions. All the features will remain same in application.
Then it should be fully functional, just with the provision of not creating content for profit. But you can double check the EULA before purchasing.