Core 2 duo was a cpu product line ran by intel in which the 2 cores run together as a pair, it means the cpu can only scale by a pair of cores at a time. It was also a line that has been book-ended by dual coe cpus. A dual core is simply a cpu with two cores which can scale up or down by a single core at a time, hence AMD's triple core cpus but not intel's core 2 triple.
As to which is better is a bit more complicated because core 2 cpus are specific to intel but both intel and AMD have dual core cpus which precede, succeed and run at the same time as them. However, if you're looking at current sockets (lga1156/1155/1366/2011) then core 2 duo/quad doesn't come into it because it was specific to lga775.