Not really that tough...
Today, the .30 carbine would be considered an "intermediate" round, following the general definition of "more powerful than a standard pistol round, less than a full size rifle round".
At the time of its introduction, the .30 carbine was not thought of as an intermediate round, although it could be considered the first one fielded. It was considered the "carbine" round, and in a class by itself. At the time, the defintion of intermediate round had not been formed the way it was a few years later.
The Carbine round was rather unique (although some very similar rounds from Winchester had been in rifles since around 1907). Yes, we did lead the pack, so to speak, with our short .30 caliber (and had even pioneered the idea with the Pedersen device during WW I, although it was never fielded), but at the time, we weren't thinking in the terms of "intermediate" that we later came to adopt. It wasn't until after the 7.92x33mm came to our attention that we created the definition of intermediate power round, and then decided the .30 carbine fit it, also. Just as some years later we decided the 5.56mm(.223) also fit in the category, even though it is an oddball compared to the majority of intermediate rounds because it does not share the common WWII era infantry rifle bore size.
In general, intermediate class rounds have the same bore size as full power infantry rifles, with a smaller case, shooting a lighter weight bullet at lower velocity. There are exceptions, most notabley the .30 carbine and the 5.56mm which have been put in that class because of overall power and also because of the primary rifles they are used in.
The .30 carbine is on the bottom end of the power range, being closer to a pistol round (like the .357 Magnum, but still clearly a step above the military pistol rounds used as the standard in WW II), and the 5.56mm and the 5.45mm Soviet round are in there, due to the lower energy of the small bore bullet, compared to the full size .30 caliber rounds used earlier.
Its not a hard and fast defintion, with clearly defined limits of bore size, bullet weight, case size/shape, velocity, etc., but a general category to indentify military cartridges, based on the general use cartridges from WWII.
Soemthing more powerful than a 9mm Luger, .38/200, .45ACP, 7.62x25mm, but less than the .30-06. 8mm Mauser, 7.62x54R, .303 British, 6.5/7.7mm Jap, 6.5mm Carcano, Swede, etc. Military rounds, not sporting rounds. Many sporting cartridges do fall in that range, but were and are not thought of as 'intermediate power rounds" the same way.
I do not think reduced power loading of the standard cartridges, for better suitability in carbines (like the carbine load for the .45-70) or full auto fire in certain weapon designs (like the CETME you mentioned) would not be "intermediate cartridges", they are "reduced loadings" of standard cartridges, because they are using the standard round case.
Getting back to gun terms that don't go together, another one (IMHO) is a "safety" on the trigger. Its NOT at safety, its a trigger activation switch!