I heard about the Stack Overflow API. Is there a Stack Overflow API available. Or is it the same as the Stack Exchange API?
They are one and the same.
When the API was first announced (March 31st, 2010), it was temporarily called the "Stack Overflow API" -- even though Jeff said that the API would be "for all the trilogy sites".
Two month's later, when stackapps.com and the public beta were announced, the official name was already Stack Exchange API. There is no separate API just for Stack Overflow.