Terry's fighting style is more of a Brawler that takes things from multiple styles. Ryu/Ken are based on Karate but with extra over-the-top stuff added in.
Terry's got an Axe Kick(Crack Shoot), a Dash Punch(Burn Knuckle), a Rising Knee-into-Dive Punch(Power Dunk), and his Projectile(Power Wave) travels along the ground. And whatever the heck you would call Rising Tackle. I guess an upside down Lariat, that sends him flying.
And those are mostly his staple moves. There's other attacks he uses on occasion like Power Charge(A Full Body Tackle), and Fire Kick.
The big similarity between Terry and Ryu/Ken is that they are pretty easy/pick up and play to use in the series.