here's something to skim, I'd never really read all of it though:www.anthrocon.org/about-furry
"Anthro" (walking on two legs) characters are the most common sorta thing but I feel like everything kinda counts. Being a furry DOES NOT have to include costumes/fursuits. Many people are completely art based and don't attend conventions or even bother with the costuming side of things.
HOWEVER it mostly depends on if you decide to identify yourself as one. Personally I am a furry, I just don't go around telling people openly because unfortunately people get the wrong idea unless they too are a furry. That or you have to explain and that's idk... lol