Bothe the FTDI and AVR chip divide their respective (and different) clock frequecies by internal divisors until they get a new clock to use for the serial communications interface (UART.)
For example, to run the UART at 9600bps, the AVR divides 16MHz by 1667 and the FTDI divides 12MHz by 1250. (it's a bit more complicated than that, but that's the general idea.)