@ Karlos
Here is a picture of a .38 Special and a .22 Long Rifle cartridge. The .22 short in the story will be the same calibre but a shorter case. It is therefore less 'powerful.'

Don't worry about what sort of bullet is loaded in that cartridge, generally they will either be lead like the .38 seen there or they will be lead but with a jacket (like what you see in the movies). The .22 bullet in a short or long rifle case is never jacketed. That copper look you see there is a 'wash' that can be scraped off even with your fingernail.
At the back of the cartridges there is a difference between centerfire and rimfire:

These are live cartridges. The .38 has a proper central primer cup and the .22 has no obvious primer, but there is primer compound inside the rim. The location of the primer in each case is arrowed. In the .22 the primer compound will be in the rim all the way around the base. Those imprints on the bases of the cartridges identify the manufacturer and have nothing to do with primers.
Here you can see where the firing fin of the gun in each case has hit the base of the cartridge in order to discharge it (arrowed):

And here is a longitudinal section through those cases to show the difference between the two primers. The main capacity of the case is for the gunpowder (not shown):

It is very unlikely that you can set off a cartridge by dropping it on the ground. However I wouldn't do it. If you find a cartridge like that, it will be impossible to manually pull the bullet out with your fingers. They are crimped into the case and have to be fired out or extracted with a tool. These cartridges are safe to handle, and even if you were able to discharge one by hitting the back with a nail, it wouldn't go very far because it wouldn't be in a barrel where it could be propelled for any length of time by the gases of combustion.
So what do you do if you find one of those?
1) Get a clear plastic bag and pick it up like a dog turd.
2) Don't touch the case, because you might leave fingerprints on there.
3) Don't touch the cartridge with any tools and avoid unnecessary handling. Forensic tests can match that cartridge to a gun if it has been chambered and then unchambered.
4) That item could be evidence in a crime and you definitely don't want to add your prints or make extra impressions on that.
5) When the cartridge is in the bag, call the police to collect it (saves you a trip).
If you find a firearm: well that is a whole different kettle of fish...