Multi-page bi-folds / booklets / catalogs - Booklet design
Most catalogs, corporate profiles and presentations are booklets - short books, usually having a paper cover.
A booklet is, technically speaking, a set of multi-page bi-fold brochures that are bound together. The term "booklet" implies more than one sheet of paper.
A way to see it is that booklets are created by binding bi-fold brochures together - usually by stacking and stapling them. By stacking and binding bi-fold brochures, you can create an 8-page booklet (2 bi-folds), a 12-page booklet (3 bi-folds), and on. Each bi-fold brochure adds 4 new pages to the page count.
Most people would use the word "brochure" as a synonym for "booklet", so if they refer to an 8-page brochure, they are in fact referring to an 8-page booklet. However, please note this may not be true in all cases.
Booklets are usually printed on high quality stock, and their morphology allows eye-catching, impressive designs. The front and back covers are sometimes printed on a thicker stock.
Booklets with a high page count are bound using other more sophisticated binding techniques, like "wire-o" binding or "perfect" binding.
Binding methods and their implications
Saddle-stitched / stapled: it's by far the most popular binding method. It's cheap, looks nice and it's fast for printers. Printers will use stapling for brochures whenever possible, even up to 40+ pages, though this depends on paper stock thickness.
Wire-O: popular for more inter-company presentations. May work better for brochures with more pages, but may look informal. Wire-O binding allows to have page counts divisible by 2, rather than 4 as with other binding techniques. That is, you can have a 10-page or 14-page bi-fold brochure.
Perfect bound: the ideal choice for brochures with a high page count. This is the binding technique used for most books, and it adds a "spine".
Booklet sizes and formats
As with bi-fold brochures, the standard booklet is LTR-sized (folded, closed), and 17" x 11" flat open. In non-US markets, they would be the corresponding DIN-A sizes (A4 folded, A3 flat open).
However, there are booklets of any size. Small booklets are usually half the standard booklet size: 5.5" x 8.5" folded, LTR size flat open.
Some booklets may also include one or more pockets or flaps to hold business cards, datasheets, etc., even other brochures. Also, small-format booklets became widely known as the companion to CD or DVD media, the famous CD booklets and DVD booklets.