Hardcore damage damages the car quicker, more and heavier.
Punctures are much more likely.
Radiator damage will damage the engine (at least) quicker, but not sure if "normal" damage has such an effect.
My experiences with "normal" damage are most of the time, that I don't get serious/noticable damage at all, when I don't crash like crazy against trees and stones and such. Several times.
But I rarely play My Team these days, mostly only dailies, wich is only 1 stage.
Rarely have anything else than light body and wheel geometry damage. Sometimes light radiator damage.
90% of the time I race with hardcore damage, because almost all clubs I'm in use this option.
And even this is not really realistically hard as it should be.
Punctures are (by far) the biggest problem here, happens quite often to me.
Radiator (and therefore later on engine) is the second most problem I have.
2-3 hits against a tree or anything else concrete damage the radiator enough so you get engine problems over time.
The longer the way to the next service, the bigger the problem you have.
Missing lights is also a problem. Any hit on the front can wipe them out.
But you won't get random damage that isn't your fault, if you that mean.
Any damage has a cause hitting something.
The only thing is maybe the wipers on heavy rain stages. They stop working for a while sometimes.
That's either a bug or part of the "unexpected moments"-feature, not sure.