From left to right, .22 CB, .22 Short and .22 Long Rifle (LR) cartridges.
Public domain image.
The three cartridges in question are (from left to right), .22 CB, .22 Short and .22 Long Rifle (popularly known as .22 LR). Now imagine that you have a firearm that is designed to shoot .22 LR. Will it be able to shoot the other cartridges?
To answer this question, we must first note that these are rimmed cartridges, i.e. the rims of the cartridges are wider than the body of the cartridges. Also note that although the overall lengths of the cartridges are different, the diameter of the cartridge cases and bullets are identical. Also, the sizes of the rims in all three cases are identical.
Now, when we first started talking about headspacing two days ago, recall how the headspace for rimmed cartridges is measured.
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That's right, for rimmed cartridges, the headspace is measured as the width of the rim. Therefore, a firearm that can fit a .22 LR cartridge (the longest of the three) can also comfortably fit a .22 short, a .22 Long and a .22 CB. Since all these cartridges have the same rim diameter and rim width, they also headspace correctly. This means that a .22 LR firearm can fire these without the fear of case separation occurring.
Of course, a few caveats must be noted here. The first is that of the .22 Short, .22 Long and .22 LR, they were all originally designed to use the same propellant, black powder, with the .22 LR having the most quantity in the cartridge (the .22 CB is even more low powered than these three). Therefore, a firearm designed for .22 LR is strong enough to handle the pressures generated by the other cartridges. Also, since the .22 LR is the longest of the four cartridges, the other three can fit in the chamber. Since all four of these are rimfire cartridges, the same firing mechanism can be used for all of them. However, it must be noted that just because a firearm designed for .22 LR can be fired with any of these 4 cartridges does not mean it can function after that. For instance, cartridges may have to be manually fed in one at a time, because a .22 LR magazine may not feed the other cartridges properly due to the different lengths of the cartridges. Also, the recoil forces generated by the smaller cartridges may not be enough to cycle the action of a firearm designed for .22 LR properly. Therefore, depending on the type of firearm and its action, the user may have to manually extract and feed smaller cartridges. The sights will also have to be adjusted, since the smaller cartridges have less power and shoot at lower velocities. Hence, while it is possible to safely fire .22 CB, .22 Short, .22 Long and .22 LR out of a firearm designed for .22 LR, there are many reasons why people do not always do so.
One more major caveat -- there are other so-called cartridges in .22 caliber, for instance, the .22 Magnum (a.k.a. .22 WMR or .22 Winchester Magnum Rifle). This cartridge cannot and should not be fired from a rifle designed for .22 LR. For one thing, the two cartridges are actually of different diameters and lengths. On top of that, .22 WMR uses much stronger propellant that .22 LR and therefore generates higher pressures (which is the reason why they increased the diameter and length of the .22 WMR cartridge, so it cannot fit into a .22 LR firearm chamber, otherwise it could be a dangerous situation because the .22 LR firearm may not be able to handle the higher pressure). A .22 LR cartridge can fit in the chamber of a firearm designed for .22 WMR, but since the cartridge is of smaller diameter, when the cartridge is fired, it may split in the chamber and stick to it.
Therefore, it is always a very good idea to always know the exact ammunition type of a firearm.