There are different sockets because of improvements in socket design. For example, compared to the older Socket 478, the almost-commonplace LGA 775 socket allows for better heat dissipation with the inclusion of a lid-like plate, which ensures that the processor is completely level and makes complete contact with the HSF on top, while also keeping the CPU fixed in place and not covering all of the CPU's surface. Also, the HDI is connected onto the mobo so as to provide better heat dissipation.
As for performance difference, no, Socket 771 borrows a large number of its designs from Socket 775, except for a few minor variations and the fact that 771 was designed for boards with multiple CPU sockets.