Have you completed the BAE course? That actually goes into detail of the difference between the app profile and the app document :-) If you haven't yet signed up to the course, would highly recommend it (https://www.pega.com/insights/resources/business-architect-essentials-72). I'd also suggest going into your App, and running all 3 types of Docs (app profile, app document & spec document), I find that's a good way to understand whats happening...
High level explanation of the two you are asking about below:-
Application Profile:- Describes the application you're going to build (basically your scoping document). It should include assumptions, requirements, and specifications, along with project details such as project participants & an exec summary.
Application Document:- Describes the elements of the app, such as process flows, user interfaces, and decisions, and can help create training guides for end users ahead of the go-live date. Best practise is to generate at each major milestone.