What do the fish do?

In the Squid Jump mini-game in Splatoon, there are randomly different fish scattered throughout the level. Example (from Wikia):

It is obviously what the red fish does: giving you a high jump boost. However, in later levels there are different colored fish. I only saw white ones, but I have no reason to assume it stops there. There was no apparent effect when I touched this fish.

So, what fishes can I encounter in which stages, and what are their effects?

The red fish cause you to instantly jump really high (typically a few platforms up).

Jellyfish cause you to be able to double jump for a short time. Hitting another jellyfish after you've already used your second jump without touching a platform will allow you to execute another jump.

Starfish cause you to charge, jump, and fall much faster for a short time. If the starfish effect ends while you're accelerating upward, you'll jump much higher than usual.

Note: The Jellyfish and Starfish effects cannot be combined, so touching one while affected by the other will replace the first effect.