To add to what everyone is saying the AFL was founded in I believe 1960 and prior to the Jets beating the Colts in Super Bowl III was never considered remotely close to the NFL in terms of talent. The first two Super Bowls between Green Bay and the Chiefs and Raiders respectively proved what everyone believed with the Pack trouncing both of them.
As someone pointed out they finally merged in 1970 after the Jets and Chiefs (against Minnesota) showed the AFL was starting to catch up to it's older and more prestigious predecessor. I don't think they started regular season play between NFC and AFC teams though so it was a gradual process.
Before the first Super Bowl there were just NFL and AFL Champions or simply just NFL Champions (if you go back before 1960, with the exception of a couple other failed attempts at an AFL and other competitors). The 9 championships we won prior to the 1966 NFL season are not Super Bowl victories because there was no Super Bowl. The emergence of the Super Bowl simply marked the restructuring of how the NFL champion is decided, much like the introduction of playoffs in the early 30s (before that it was merely who had the best record when you dropped ties from the record). Thus we are 12 time champions, 3 of which are Super Bowls.
Born and bred a cheesehead