Yes, Stan is supposed to be Trey and Kyle is supposed to be Matt but there's obviously some differences. Cartman and Randy also represent him to a lesser extent. also Mr. Garrison. Stan, Cartman, Randy, and Garrison all have this thing in common where they use absurd outbursts to cover up their hurt feelings (except Cartman does that by default so it's actually convincing since it doesn't stand out when he does it), and that's basically South Park. Like South Park is full of all these emotional touching moments followed by some crazy humor. It's like 'no homo' except instead of gayness it's with feelings. Like that entire Kenny Dies episode is liek these sad moments but then it's like haha wacky abortions and fetuses.
"Fuck you, Kyle, you're a piece of shit"
"Kyle, I love you"
"You're a piece of shit though fuck you"
"I love you"
that's it that's the essence of South Park
Cartman pretending he's sad that he's part ginger when he actually seems to genuinely care about not having a father. I swear to god Trey Parker like expresses his feelings in South Park but he's kind of embarrassed so he covers it with comedy. That's why South Park has all this dark/black humor, but doesn't feel at all nihilistic/cynical like Family Guy or Robot Chicken or whatever, the black humor is like a coping mechanism or something. maybe I'm just reading too much into this.