Basically first class and priority are the same class of service.
First class however, is not distance sensitive, one stamp is good to send your mail next door, or from Florida to Alaska. The example pricing sheet goes up to 13 ounces.
Priority mail is zoned, the further away... the more you pay. The example pricing starts at one pound, and one pound is the minimum for “Priority”.
Ah, no, they're not. Not even close.
Leave it to the ignorant to single themselves out. You did good.
My post office denies first class service up to a certain weight. Has to go priority if it is a package and not an envelope (and no I am not talking about using their priority boxes they provide).