They actually arent a type of PCI, it's PCI-E (two separate types). PCI-E 2.0 is just a newer version of the PCI-E bus, which from what i've heard doubles the bandwidth of the bus.
Yes you can use a traditional PCI-E x16 video card in a PCI-E 2.0 x16 slot, and vice versa. Currently only the Intel X38-based motherboards and AM2+ support it.