Is there a difference between net damage and meat damage?

Not really. It's just that some cards only prevent meat damage while others prevent net damage.

But 1 meat damage and 2 net damage equals 3 damage overall.

They both do the same thing. There's a thematic difference in that meat damage tends to require a successful trace or a tag because the Corp has to know where you are (to send someone to punch you in the face) while Net damage is dealt through the network, so it's often more of a reaction to a run but there are enough exceptions to that to make it more of a flavour thing. They can be prevented through different cards, though.

Thematically I think it's more down to where it happens - meat damage happens in the real world, and net damage is attacking the Runner's avatar in the net (a la The Matrix).

Mechanically, it's as others have already said - the only difference is in which other cards interact with them (prevent/avoid or triggering from them).