Circa 1930, the new Soviet military sidearm was modeled after John Browning designs. The recoil and locking mechanism, magazine holdopen, firing pin, etc. were very similar in principle to the American standard 1911/1911A1. The lockwork and cartridge feed arrangements were more original. The gun was chambered in 7.63mm, but Tokarev apparently found it expedient to respecify the case dimensions and tolerances, perhaps to suit production machinery already available in the Russian arsenals at Tula, Izhevsk, and Syestroretsk. So nominal dimensions of 7.62mm Tokarev and 7.63mm Mauser cartridges aren't identical, but they're mighty close. The apparent caliber difference - 7.62mm and 7.63mm - is nominal only. That is, the actual dimensions of bore and bullet were identical, but the Mauser cartridge had been given a name which would differentiate it from the 7.65 and 7.62 cartridges of the time. The situation is much like rifle cartridges, in which, say, .22-250, .222, and .223 are all the same actual caliber.
'Way back then, Russian small arms - 1891 rifles, 1985 revolvers, 1910 machine guns, 1941 and 1943 submachine guns, 1938/1940 Tokarev rifles, 1930/1933 Tokarev pistols, Simonov rifles, etc - were all of .30 caliber and had identical rifling. [Memo to self - document this!]. This allowed the Russians to use the same boring and rifling machinery for all small arms. Larger guns, such as the 1938 Degtyarev DShK in 12.7mm (suspiciously similar to the .50 Browning cartridge), obviously weren't made on the same machinery.
As produced by Russia, 7.62mm Tokarev cartridges were loaded to the same velocities as 7.63mm Mauser cartridges, and used the same bullet.
There is a theory that because the Mauser magazine was machined as part of the frame, and so was more rigid than the sheet metal Tokarev magazine, Mauser cartridges were subject to more severe battering under recoil than Tokarev cartridges. To prevent the bullets from being pushed into their cases, Mauser cartridge necks were staked with three crimp marks, but Tokarev cartridges could get by with the more conventional crimp. Historically, this theory doesn't seem to hold up. In the pre-Tokarev days, Mauser cartridges could be found with at least three types of crimp - three stakes, conventional crimp, and a particularly secure crimp into a bullet cannelure, a method used by, I think, Kynoch.
The Tokarev cartridge was adopted postwar by Communist China for the Type 51 and 54 pistols, the Type 50 submachine gun, etc - all copies of Russian guns. It was also adopted, doubtless under duress, by Warsaw Pact countries. The Pact countries were Poland, Czechoslovakia, Bulgaria, East Germany, Hungary, Albania (until 1968), Romania, and of course the USSR. (Note that Yugoslavia was never a member). The Warsaw Pact was an arrangement whereby in case of war with the counter-revolutionaries (ie, the West) national armies would be placed under Soviet command. The Soviet Union wanted common ammunition, but didn't require that the guns be identical to Soviet models. So some countries, most notably Czechoslovakia, adopted indigenous gun designs which used Soviet ammunition.
The Czech situation is complex. A large number of submachine gun designs are of Czech origin, dating from the 1930s to today, but most were intended for export sales and were never adopted by the Czechs themselves. The Czech army used submachine guns in 9x19mm until the country fell to the Communists in 1948. After that, the army's submachine guns, the Models 23 and 25, were redesigned to take Soviet 7.62mm ammunition, and became the Models 24 and 26. The later Model 61, the Skorpion, was unrelated to these, and was always in 7.65mm (32ACP). The Czechs loaded their 7.63mm ammo to higher velocities than standard Tokarev. One edition of Hogg & Weeks (Handguns of the World, 2nd ed) called that heavier loading Czech M48, but later editions deleted that sentence [memo to self - verify this].
The 1952 Czech pistol was supposedly designed for this more powerful cartridge loading, but that seems odd as the Vz 52 is a rather flimsy pistol (although the locking arrangement is strong enough). Commercially loaded Czech ammunition (Sellier & Bellot Tokarev) is noticeably hotter than historical 7.63 Mauser ammo, at 1647 ft/sec vs. 1400 ft/sec or so.
Ezell, Small Arms of the World (12th ed, basically the old Smith book with Smith's name dropped off) - which is not 100% reliable - lists 1640 ft/sec for the Russian PPSh41 (with 10.6 inch barrel), vs. 1800 ft/sec for the Czech Model 24 (with 11.2 inch barrel). In other words, one cartridge (Tokarev), two different velocities from similar barrels. The question of which Tokarev is hot, and which is not (or, more importantly, which is too hot), has yet to be answered satisfactorily.