Well, the first two are right, but the third is (technically) wrong. The only people that really ever say "fishes" are scientists, and even they dont say it all the time. Its like deer and moose. They can mean singular or plural depending on the other words used in the sentence.
I saw a moose. The letter "a" tells us that the next word is singular.
I saw some moose or I saw a lot of moose is plural, because the words in front of moose modify it to go from singular to plural.
So, in your example, if you wanted to tell someone you caught 2 different species of fish, you would say I caught 2 different fish and if you caught multiple fish, and it doesnt matter if the difference is specified, you could say I caught some fish.