Could you please help me understand where they're exactly used and tell me if there're any distinctive features?
Is 'prospectus' only used for academic centres?
It has lists of something -- like a library catalogue (with list of books owned by the library), or a catalogue of things you can buy at IKEA or some other store (these are thick and usually are released on per-season basis as opposed to a flyer or brochure)
Brochure is just a small pamphlet. It usually contains some information or advertises something.
Leaflet is just one page. It also contains some information or advertises something.
We also have flyers. These are sent out by the stores every week to advertise their weekly sales.
Prospectus is used by businesses more than by "academic centers".