The Tamagotchi Nano is a very small, simple Tamagotchi with a limited number of characters and only one game. It's fun to play with but they're more like keychains than actual virtual pets due to their lack of features.
The Goldfish Nano is just one of the designs and isn't different from other Tamagotchi Nanos.
^^They are. However they do have a game (catch the letters to spell "Tamagotchi"--don't worry; it's in English, two times for perfect score). And they are cute. They're almost round, kinda like a Tama Go, but much smaller. They're great for the cuteness factor.