At first glance, yes, he is just another guy with a tragic past. However, in theory, you could say that about a lot of characters if you really wanted to.
What separates Terry from other fighting game characters (specifically SF characters) is that he actually shows development throughout the games and is relatively realistic. It's true that the basis for his story is revenge for a murdered father, which isn't uncommon at all. He spends his life training to become a fighter to get revenge and along the way he meets new friends etc, etc. I'll admit that's nothing original.
However, I feel that his design reflects how living that kind of life would be. A huge part of Terry's character is that he's poor. He didn't have anyone to look after him, next to no friends/family and he spends all of his young adult life training to get revenge, as opposed to getting an education like a normal child his age. He eventually becomes one of the world's greatest fighters, but at the cost of a normal life. He doesn't have a home, no car and no job. Not to mention the massive amount of guilt he gets from "killing" (he knocks Geese off a building but Geese refuses to be rescued by him and let's him self fall to his death) his once hated enemy and the lack of satisfaction he gets from doing so. The only saving factor is that he is able to adopt a kid in this ordeal to help give his life meaning.
Even his classic outfit fits him perfectly. It's iconic and works well with his backstory. It's minimal yet it says so much. He's a fighter, which can be seen with the gloves, the torn sleeves on his shirt and his minimal jacket. His blue jeans and red cap show hint at the fact that he's American. The simple design shows that he's kinda poor and that he doesn't really care about bells and whistles. His moveset accompanies his design by showing off his street fighting background. He lacks many karate/kung fu, opting for more aggressive attacks in favor of flashy moves. A lot of his gameplan involves rush down and applying pressure, kind of like one would in a real street fight.
I believe that Garou: Mark of the Wolves is what really separates Terry from all other characters (in case you didn't know, Garou takes place 10 years after the death of Geese Howard) and everything about his appearance in that game actually shows development. Unlike every returning SF2 character in 3rd Strike (which is comparable since both games take place in the future of their respective series), Terry actually changes his costume. Now this may not seem like much at first, but I think a lot of effort went into designing his new outfit because I think it fits perfectly, and here is why.
1.) His new design shows maturity. He cut his long, got rid of the hat and got a new pair of shows. Instead of a torn t-shirt and a sleeveless red jacket, he actually wears a normal t-shirt and a more elaborate bomber jacket. This new attire gives him a more respectable and formal look, which matches his age.
2.) His design still looks like Terry. Although his hair is shorter and his jacket is flashier, the fact that he keeps the gloves and wears a pair jeans and t-shirt show that he's still a fighter. He may not do it as frequently as he used, but he still has the experience and can still hold his own if he needs to with this new outfit design.
He's also raising a kid now, which is uncommon in fighting games. There's Ken, but we don't really see too much interaction between him and his kid, unlike Terry and Rock where they're practically rivals. It's an interesting relationship; Terry has taught Rock much of what he knows about fighting but won't let him win just because he is his son. He wants to see his son succeed, but he just won't let him win because he raised him. He's become the father that he never had.
I could also throw in more stuff about his romance with Blue Mary and his relationships with other fighters, but I need to get some sleep. I just think Terry's really interesting for a fighting game character.
