Does lag affect the game worse in CoD4?

Ok, in CounterStrike, if you are lagging a little bit, aim at a guy's head and shoot, you actually shoot him in the head.
But in CoD4, if you want to shoot a moving target in the head, you have to lead him and shoot where his head is about to be.
Is this what is going on?
In counter-strike, when you shoot at a guys head, does it register the hit on your computer, and then send info to the server that you shot the guy in the head,
While in CoD4, when you shoot at a guys head, does it sends to the server only where you shoot, and then the server decides if the guys head is there?

that's what I would think is going on, because if you want to hit a guy running to the side, you have to lead him a little bit to account for lag...

Also, I am comparing counter-strike on pc to CoD4 on xbox...

Lag doesn't do much on the PC. If you have like 200 ping if affects your sprinting, but that's about it.

Lag has always been a serious issue with CoD games. I read a big article on why they have worse than normal issues with hit detection -> lag, but cant remember where it was. It was something along the lines of what you said in how the packets were sent. The good news is, its fixed much better than CoD3 as it was the worst of all of them. There was times on CoD3 where I would shotgun two people, they would turn around and shoot me and my buddy, then both would die and I would get credit for it. :-/ At least this one just has a small hit detection lag.

antilag?