If you see ammo elsewhere, it's properly .22 WRF ("Winchester Rim Fire, IIRC), and not the ".22 MRF".
"M" generally denotes a magnum case, in rimfire ammo - which is why Winchester designated the newer/longer loading the .22 Winchester Magnum, using ".22 Win Mag" on their boxes, and others like CCI use ".22WMR".
Some old-timers refer to the WRF as the .22 Special, because it fits the longer .22WRM chamber just like the .38 & .44 Specials fit their longer respective .357/.44 magnum chambers.
Remington actually loaded their version with 45gr slugs as the ".22 Remington Special", once upon a time.
When I use it as a mild load in my magnum rifles, the POI difference usually requires a sight adjustment - not conducive to ammo switching in the field.