The one on the left looks like it is an iron based alloy and the one on the right looks like a copper based alloy, which would explain the difference. Copper is much denser than iron, so more atoms can fit into the same area, which causes it to be heavier(atomic weight, mass, etc. also has to do with it).
I get several of these in change each week. It's still the most common date of 2p coin in circulation!
I can't explain the weight difference - officially it should weigh 7.12g, but there must be a certain amount of tolerance and in 1971 the quality control was probably not that great as they just wanted to get hundreds of millions of new coins out as quickly as possible in readiness for Decimalization.