Bears are fat and can be either somewhat hairy or very, very hairy. It's more indicative of someone who's chunkier, though.
ROFL although that might be the meaning/stereotype today, it's not what the term Bear actually meant back when it was first coined in SF 1987. It has a much broader brush stroke than just a fat guy who's hairy.
Bear was coined as a term to mean someone who doesn't follow the "gay stereotype" and back in the late 80's those stereotypes or gay trends we rebuked were: We didn't go to the gym every day. We didn't want to shave our mustaches, beards or body hair. We liked other music besides dance, techno and whatever was playing in the clubs. We actually enjoyed sports.
Here's a good example. Back in 1990 after getting off of jury duty I went into the "Bear" bar in San Francisco. Inside they were playing Pink Floyd's "Dark Side of the Moon."
We were guys who didn't want to change what we liked in order to fit in with mainstream gay culture. I like sports, I'm a huge baseball and football fan. I like many different types of music but mainly hard rock, heavy metal and alternative. I hate walking into a gay bar and hearing the normal deafening thump of the latest dance music. I actually like body and facial hair.
These days there are bears, cubs, muscle bears, otters, teddy bears, grizzly bears, polar bears etc.