Yes, a motherboard can usually run different speeds for the FSB. But that doesn't mean that CPU FSB speed would be any different from the speed at the chipset side (Northbridge to be exact). When you change the FSB speed in a motherboard's BIOS, the CPU and Northbridge run at the same speed. It wouldn't make any sense to drive different speeds on both sides of the bus, because that wouldn't work properly. There is even a performance loss when running the memory at a different speed than the FSB, but that's a whole other story.
Newer CPU's - read, those not from more than a decade ago - have the Northbridge built-in, so there is no separate chip to make a separate bus to. Although technically there's still some kind of bus, but not an FSB, because everything happens right on the CPU substrate (if not the DIE itself).
I hope this makes it more clear.
Regards
Dalai