SPD refers to a type of clipless pedal. Clipless pedals use special shoes with special cleats screwed to the bottoms of them to get your foot securely attached to the pedal. The cleat clips into the pedal and is disengaged by twisting your heel outwards.

Clips refer to another way of getting your foot more securely attached to the pedal. Here, a meta clip screwed to the platform of the pedal, usually combined with a strap, helps keep your foot planted where you want it.

The idea for both is a more secure footing on the pedal and therfore better power transfer to the drivetrain. Some people prefer clips for various reasons, but I think one can generally assert that overall clipless is going to be more secure and probably more efficient. Both are going to give you better power transfer than straight up platforms without any retention mechanism.