.22LR, the modern standard
.22 Short, .22 Long, CB caps, and others are still around, but not common anymore. The .22 WRM (.22 Magnum) is a longer round, with a larger diameter case, and will not work in anything other than a gun chambered for it. And smaller rimfire rounds should never be used in .22 Magnum chambers.
A gun chambered for the .22LR will fire all shorter .22RF rounds, the long, the short, and the CB/BB caps. If you put them in the chamber, they will fire.
What they will not do is feed in box magazine feed repeaters, or cycle (reliably) tube mag semi autos. Revolvers will shoot them all. (NOT the magnums)
Yes, chamber cleaning after firing shorter rounds is needed.
"standard" velocity .22LR was the normal round for decades. Today what is most common is "high velocity" or "High Speed" .22 LR ammo. "Standard" velocity ammo is today usually only found as target or match ammo.
To further complicate the issue, there are "hyper velocity" rounds common today, having a higher muzzle velocity than "high velocity" .22LR. These can be fired in regular .22LR chambers, although some guns don't like them much. Rounds like "Stingers, Yellowjacket, & Viper" are in this category.
There are also sometimes found obsolete rimfire rounds, such as the .22 Auto. These are not interchangable with any other rounds, and should not be put in .22LR guns, even if you can somehow get it to fit.