Is a woolly bear really a bear?

No. Its really a catipillar. Its called a woolly bear because of of the fur covering its body looks like bear fur.

No! It is not a bear. Woolly bears are the nickname for a type of caterpillar of the Arctiidae family. They are called "woolly bears" because they have a dense furry covering. After they come out of their cocoon, they become tiger moths.

It's the only time in nature when a bear can grow up into a tiger!

Just like a real bear, you probably shouldn't touch a woolly bear. Though it may not have teeth or claws, its soft looking hairs can sometimes sting you.