Recoil-driven delayed-blowback pistols have an explosed "slide", which also houses the breach block. They fire from a closed and charged chamber (i.e. slide-forward and loaded). When you pull the trigger the hammer hits the firing pin which starts the fire/load cycle.
Recoil-driven delayed-blowback SMGs do not have an exposed "slide". They have an enclosed "bolt" or "breach block" that travels back and forth within a housing. This is make it more reliable, a failure less fatal, and to make cooling airflow directed (the bolt/block can push and pull air through vents). Also makes it safer because rapidly moving parts are not exposed where they could find dirt and clumsy fingers. Recoil-driven delayed-blowback SMGs usually fire from an "open bolt" (i.e. bolt-back and unloaded) which means that the trigger releases the bolt, which moves forward via a compressed spring, strips a round from the magazine during it's travel, chambers it, and a delayed cam hits the firing pin which fires the round, recoil drives the bolt backwards, ejecting the empty casing, compressing the spring and the bolt gets locked in the back position.
Firing from a bolt-back position means that on fully automatic the bolt moving forward can counter muzzle-climb from the previous shot. However for single shots it makes them less accurate as the muzzle drops on the first shot fired.
It is rare for a recoil-driven delayed-blowback SMG to fire from a closed bolt. It makes it mechanically more complex and requires more maintenance. However, with that comes increased reliability, and first-shot accuracy. This is why the H&K series, most notably the MP5, were the darlings of CRW/CT/Hostage Rescue the world over.
Converting a pistol to fully automatic is a dangerous task. For most automatic pistols this involves simply removing the sear spring; which means as the new round is chambered and the slide goes forward the hammer drops again rather than staying held up. Auto pistols are not designed for fully automatic fire. The slide can come off, they can overheat very rapidly, and they have incredible muzzle climb and recoil due to their light weight.
There have been experiments in the past:
The Beretta M93R was a modified M92. It was made in 9mm Parabellum. It was limited to a 3 shot burst because it became uncontrollable on full auto. It had an extended barrel with a muzzle brake (recoil compensator that directs gases upwards and outwards to stabilise the muzzle) and a folding foregrip in front of the trigger guard to make it controllable with just a three-shot burst. It had a detachable stock to try to make it accurate.
The Colt Scamp was experimental. It was made in .22LR (rimfire). It is the weapon used by the original Robocop. It was limited to a three-shot burst for controllability and you can also see metal weights under the barrel to stop muzzle climb. It also had a muzzle brake to aid this. It never took off.
The HK VP70 in 9mm Parabellum was a chunky single shot pistol that when attached to its detachable stock could fire a three-shot burst. It was weighty to reduce felt recoil. As an SMG it wasn't enough firepower, as a pistol it was too chunky and heavy.
The Glock18 in 9mm Parabellum was a fully automatic version of the Glock17. No extra weight, no detachable stock, no foregrip, no muzzle brake. It was pretty much uncontrollable and I've never heard too much about it. It sounds like something very special for very special purposes.
The Stechkin in 9mm Makarov was a fully automatic version of the Soviet police/military Makarov sidearm. It could have a detachable stock and had a slightly longer barrel but was otherwise identical to the Makarov. It was made for covert operations and was, I believe, well regarded for that purpose.
The Mauser 1930 (or "Schmizer Pistol") in 9mm Parabellum is possibly the most successful auto-pistol conversion in history. It was made in 9mm Parabellum and was a covnerted form of the 9mm version of the Mauser 1896 ("Broomhandled Mauser") which came in 7.63 Parabellum (later known as 7.62 Tokarev). It could carry 30 round magazines, was very reliable, had a high rate of fire (my grandad, a British RSM and officers firearms trainer during WWII, said it "could cut a man in half"). It had a detachable wooden stock that was hollow and doubled as a holster. There are damn good reasons why this early attempt worked and later ones didn't. The 1896 had a magazine forward of the trigger; this means that the clips that hold the magazine are more sturdy, can carry more weight (30 rounds instead of 7 to 17) and can feed ammo more reliably. It did not have a slide, but used a bolt that became exposed at the rearmost point of travel. The fact that the original pistol had most of the features of a succesful recoil-driven delayed-blowback SMG are no doubt what made it a successful conversion. It was usually issued to tank commanders for the purpose of clearing infantry from the hull and sides of the vehicle.
Other recent developments like the micro-uzi and Steyr TMP (Tactical Machine Pistol) are SMGs scaled-down to also be practical as pistols. Which they seldom are.
(The Mauser 1896 with a funny scope and plastic funnel on the end of the barrel is the weapon used by Han Solo in Star Wars. The Stormtroopers use thinly disgused Stirling SMGs with 5 round clips instead of the more distinctively curved 30 or 45 round ones. The weapon used by Princess Leia very early on is a disguised Ruger .22 target pistol.)
I know that sounds off-topic, but I thought explaining all that might make the OP realise why it most likely is not simply a modified pistol.
Certain features in the design of firearms have been long-influenced by certain features in the design of humans. That's why so many weapons have so many similar features. Other factors do come into play, like the manner and theatre in which the weapon is likely to be used. (e.g. The Stirling SMG had a side-loading magazine so that it could be used from a crouching or prone position far easier than a magazine that loaded from the bottom. The UZI had a handgrip-loading magazine so that it could more easily be reloaded in the dark, as one hand can always find the other even when your eyes are closed.)
I'll shut-up now, I think I've bored everyone to tears with my gun-geekery. (Yes, I know they are not guns because they have rifled barrels)
\\'
