Have a look at this drawing
https://www.beesource.com/threads/build-it-yourself-equipment-plans-in-pdf-format.367102/#lg=thread-367102&slide=0
If the main purpose of the box is raising brood (eggs, larva,
pupa), it's a brood box.
If the main purpose of the box is storing honey, it's a "SUPER".
"Shallow" boxes are mainly used for comb-honey.
There's another odd size, called the "California Medium" which is an
inch taller than a medium. In general, don't buy them.
That slide-show has a lot of other interesting pix in it.
Anyone with a table saw and reasonable shop skills can build those
(expensive) bottom boards, especially if you have a cheap source of
wood.
A full-size sheet baking pan from business-costco is $8 - it does
the job of a $$ telescoping cover for so much less. (the hive should
have a migratory cover or slab of plywood cut to fit)
In winter half the heat a hive (a colony) generates is lost through
the top, so Insulating the top is a big win. An inch or two of
styrofoam panel will do the job.
that's my 2¢