A few general rules
- Bolt/Lever/Pump are most likely to work with all three lengths.
- Semi-auto is least likely to work with all three lengths [unless fed as a single-shot].
- Detachable magazine-fed rifles don't 'tend' to work with all three calibers, unless as a single-shot.
- Tube-fed magazines 'may' work with all three calibers.
For a variety of reasons, I am a 'tube-fed' type of guy for my .22 rifles.
Living in California, I get more than 10 rounds legally, for example.
Only 1 of my tube-fed .22 rifles is finicky, demanding .22long rifle: my Marlin Model 60.
That said, some tube-fed .22 rifles can shoot all three calibers, all at the same time, and others require a full tube of short, or of long, or of LR.
I think the post by Gunfixr gives the best explanation of how that might be: the method of cut-off/timing.
In modern production guns, there is only 1 semi-auto I know of that is supposed to shoot all three lengths, and [supposedly] interchangeably: the Remington Speedmaster 552. It is still in production as the 552BDL.
I have the 552A [from the 1960s] and have fired Long and Long Rifle from it. I don't have the short rounds to try. And I have not tried staggering the tube mag with Long/LR/Long/LR, etc. However, it worked just fine with Long or Long Rifle.
My Model 60 won't.