For practical purposes, they are equivalent. In North American, there is a small distinction. New Oxford American Dictionary: USAGE In North America, prison specifically denotes a facility run by the state (in Canada provincial) or federal government for those who have been convicted of serious crimes, whereas jail denotes a locally run facility for those awaiting trial or convicted of minor offenses.

thanks a bunch

Also, “jail” is less formal, and “jailer” is very rare. We say “prison guard”.