Wanna is short for "want to", but NOT for third person singular.
I wanna go to Spain.
We wanna get a car.
He wants to go to Spain too.
"Gotta" is short for "Got to" and generally replaces "have to". In the third person you would use it as "has got to", generally always shortening it to 's gotta.
I gotta get a ticket. (I have to get a ticket, I have got to get a ticket)
You gotta give me the money. She's gotta come too!
My mom's gotta go to the store.