>first image is a machine pistol
>second and third image are pistol caliber carbines
>implying these are submachine guns
A pistol action given automatic fire capability isn't a submachine gun. A shortened rifle is also not a submachine gun. If those things were true, then that would necessarily imply that the Glock 18, the AKS-74U, and the Colt Commando are all submachine guns. Since all of those are closed bolt designs, two are rifle caliber, and one has a magazine that feeds into the grip, then we must assume these are all features which are acceptable on SMGs by definition and not belonging to other types of designs. By logical extension we can determine that submachine guns are exactly the same thing as rifles, and pistols, despite a full century of historical and engineering knowledge lending towards the contrary, and all the world's pioneers of SMGs disagreeing with this implication.
I'm inclined to agree with you, at least partially, although there are other things to consider such as many Slavic languages who have no original term for submachine guns and simply have a generic category for 'automatic weapons that aren't machine guns' (avtomat, samopal, etc.) which includes both subguns and carbines - in some rare cases even full length rifles. American society in general lends itself more towards a familiarity with guns, which is why we have several terms other nations and languages don't use; 'battle rifle' is a common example. Other peoples simply call it a rifle or use their 'assault rifle' analogue despite a full-power rifle cartridge overpowered and cumbersome for assault tactics.
This subject is always interesting to me because no language is as analytical about it as English, but ultimately there are so many things that blur definable lines (such as the ZK-383 which is either an SMG or an LMG, or the Villar-Perosa which is a pistol caliber aircraft machine gun) that it becomes a bit subjective and comes down to discussions of linguistics at times. It's a fun thing to autism about.
For example, the M1 Carbine is a rifle, but .30 Carbine is shaped like a pistol cartridge and performs similar to .357 Magnum… but its pressure curve was designed for the 18" barrel specifically, making it a definite rifle round.
>pistol - a gun designed for use with one hand and no need for a stock, can have the magazine located in the grip or externally (or have a cylinder, etc)
>rifle - a gun designed for two-handed use from the shoulder, magazine is not integral to the grip
>carbine - functionally the same as a rifle, but shorter
>subcarbine - ditto, but with an even shorter barrel (think AKS-74U)
>submachine gun - a small caliber automatic weapon, compact but two-handed, typically open bolt, external magazine
>machine/auto pistol - a pistol, but automatic (G18, CZ 75 Auto, Skorpion)
I call the MP5 a PCC since it's a cut down G3.
I should have added, the Skorpion blends the machine pistol/SMG distinction, but I place it as an MP in my book specifically because of its design - the Czechs tuned its shape and weight balance for one-handed automatic fire because they wanted it to serve as both a rear echelon PDW style of weapon and a sidearm to a rifle, and included the recoil/rate of fire regulator feature to make that easy. Their choice of .32 ACP was clear for that too, since they had a large amount of 9mm Parabellum in their inventory and deliberately went with a weaker, more controllable round. But, they also included the stock for ranged shooting, which helped make it a less situational gun. Really, the Vz. 61 is a very unique weapon on its own, and I can't think of another thing that compares directly to it except for - maybe the HK MP7?
Pic related is a holster for carrying a Skorpion on the hip, to enable one-handed draws.