snaps and eyelets are the same thing except there is no hole in a snap. I don't use snaps because it is easier to use a brad and the effect is the same.
Eyelets and brads are both used when you want to attach things together, and eyelets are useful when you want a hole like in a tag, or to thread some fibers through.
I prefer brads as you don't need a tool and you can use them silently, but sometimes you need the eyelet because you need the hole.
To set the snap, it is the same as an eyelet on the back, punch a hole, put the snap though, then set it with your setter.