A peach is fuzzy. A dog is furry.

"Furry" is an adjective. It means to have fur. Specifically, fur is short body hair. Animals can be furry. People can be furry, too. That's about it. "Fuzzy" is an adjective, too. It means to have fuzz. Fuzz is small or light covering. Many things are fuzzy, like clothes, carpet, and even fruit. "Fuzzy" can also mean vague, that is, the opposite of clear.

Furry things (like animals) are always fuzzy. But fuzzy things are not always furry. A rug can be fuzzy. A blanket can be fuzzy. Hats, jackets, scarves, and many other things can be fuzzy. But these things will not be made of fur and will not be ‘furry’. Also, stuffed animals and anything made of fake fur would also be considered both furry and fuzzy.