There are many ways to open a can. Marti is correct that those two operate on basically the same principle, and yes, of course the can opener opens a can, whether or not it looks like one you know.
You can use a screwdriver or (preferably, it's sharper) chisel. I have actually done this to "can-open" a barrel. Just hammer the chisel around the rim (inside, after initially piercing the top.)
There are the minimalist can openers from army rations, and the ones on folding knives.
Also the ones with a "confusing sharp part on a bottle opener/corkscrew" which operate on a similar principle.
There are the fancy new ones that cut through the seal sideways, leaving "no sharp edge and a lid that can be put back on the can" at least for cans of the right size seal (I've found ones they don't work on - which you can't tell for certain until the lid does not come off.)
There are videos out there of all of them in use (ah, what founts of knowledge the internet is reduced to bringing.)