Is fish or fishes?

Today only I know that 'fish' is also the plural for fish, but the word 'fishes' exists too, so what's the different?

The term 'fish' is used to refer singular or plural for 1 type of fish
The term 'fishes' is used to refer plural for more than 1 species of fish.

Examples:

1. A school of fish. (plural)

2. Fishes in the sea. (plural)

3. If the aquarium has only 1 type of fish, regardless of the quantity, we would say:
    "Look at the fish in the aquarium!" (plural/singular)

4. If the aquarium has more than 1 type of fish, we would say:
    "Look at the fishes in the aquarium!" (plural)