I think the operative part of the description is machine-gun, i.e. a weapon capable of automatic or burst fire. Most police and paramilitary versions of such weapons converted to semi-automatic only are described as "carbines."
As well as the MP5 converted in this way, some UK forces use carbine versions of the AuG-Steyr firing 9mm rounds.
According to Wikipedia, a Submachine gun is a firearm that combines the automatic fire of a machine gun with the ammunition of a pistol.
And a Carbine is a firearm similar to, yet shorter than a rifle or a musket. These are essentially shorter than rifles but fire the same ammunition, although usually at a lower velocity.
Another class of carbine is a semi-automatic version of a submachine gun, with an extended barrel, just over 16 inches (406 mm) long, which will escape ban by some "assault weapon" legislation. While functionally identical to other carbines, these are banned in some places as "assault weapons" based on their cosmetic similarity to submachine guns. However, they may not accept certain parts (such as magazines or collapsing stocks) from the submachine guns they resemble.
So it would support Vegetius' statement of a semi-auto submachine gun being classed as a carbine. Obviously a different sort of carbine than the M4A1 carbine rifle.