"Fish" is usually the plural and singular. I think I read "fishes" as a noun is used for some scientific purposes in labeling fish but it is not something layman use.
I agree with MagicCaspar here...los peces is plural and fishes is not gramatically wrong. Unless there's something I've missed, I think "fishes" should be regarded as correct
In biology, for instance, fishes is used to refer to multiple species of fish. For instance, if you say you saw four fish when scuba diving, that means you saw four individual fish, but if you say you saw four fishes, we might infer that you saw an undetermined number of fish of four different species.
Pescado/s is food some people eat and pez/peces are live fish. It is like pork/pig or beef/cow.
"Fishes" is used to distinguish animals of different kinds (for example, a group of tuna and swordfish), whereas "fish" denotes a group of all the same kind (e.g. a school of marlin). This distinction is usually ignored in casual speech, but it's definitely not wrong.