The sizes of supers used in beekeeping these days often are called different names in different areas and are generally as follows:
1. Dadant Deep -- is any box deeper than the 9 7/8 box, they are rarely used in the US but some areas of Europe use them.
2. Standard Deep -- is the common 9 7/8 deep box, at 9 7/8 it is called a deep regardless of frame count.
3. Western/medium -- is 7 7/8 deep and was once very popular west of the Rockies, hence its name. It is still available through Mann Lake Ltd. It is usually called a Western.
4. Illinois/medium -- 6 7/8 deep is what is commonly a Medium. Medium and Illinois can safely be said to be the same thing.
5. Shallow -- 5 5/8 deep, is usually used for cut comb or ease of lifting and 2 shallows can be extracted in the same space as 1 deep.
6. Comb -- Supers designed specifically for comb honey, such as Ross Rounds, are 4 15/16 deep and can be converted to a shallow by adding a 3/4 shim along the bottom.
If confused about super size just give the depth. But 99% if the time the word Medium is referring to an Illinois sized super.