From what I recall of 28 Days Later, where the old guy gets infected and turned with a bit of infected blood, they (or at least he) didn't have immunity to the plague, unlike in Left 4 Dead. Is this the case in The Walking Dead as well? They don't seem to be particularly careful about how they splatter the undeads' bodily fluids all over themselves (be it a rock to the head or machete to the gut).
In the comics it is established that everyone already is infected, though the symptoms only show after you "die" unless the brain is damaged too much.
This was shown with
Shane. He died by gunshot, yet turned into a zombie while laying six feet under without having endured any zombie-bites. After Rick learned of that fact, he dug him up again and killed him for good.
This also applies to the TV-show:
There was a man, who committed suicide by hanging himself in a tree, and he turned into a zombie as well. Andrea had him killed out of mercy.
The survivors have no immunity.
In both the graphic novels and the show the survivors have at least one member of their group get bitten, and start to show symptoms of the infection.
It is also mentioned that they had to take care not to get any part of the walkers, particularly the fluids, near their mouths or eyes.
this comes up particularly when they are covering themselves in walker fluids to mask their scent.
Presumably this is to reduce chance of becoming infected by contact.
This answer is based on information up through the end of season 2 of the TV series. In the episode Better Angels, we see two people die. Neither die from walkers, instead they die from human on human violence. Their dead bodies are not touched by walkers. They both return as walkers. Afterwards, Rick confirms to the group that Jenner told him that they're all infected.
In season 1's Vatos, one of the survivors, Jim, is bitten during a walker attack. In the next episode, we see that he's getting very sick incredibly quickly. We're led to believe he'll soon become a walker, an experience some of the survivors have had prior to Rick's waking up.
I think what we're seeing is that the disease that causes the walkers is dormant in living humans. Only once a human dies does the disease become active. Once active, it animates the brain stem and turns the body into a walker (as shown in TS-19). Now that the disease is active in that body, biting a living person introduces the active form of the disease to the living person's system. This disease is deadly or at least turns them into a walker quickly.
It'll be interesting to see what happens with
growing fetus in season 3.
Almost every interaction with the walkers ends with an inspection for cuts or bite marks. This suggests that the current survivors don't believe that they have any particular immunity to becoming zombies themselves. It also indicates that casual contact with the walker's fluids is not sufficient for transmission.
TL;DR: Neither. Zombie blood isn't that dangerous.
Word of God: Franchise creator, writer of the comics, and Executive Producer of both shows, Robert Kirkman:
Q: This is a real Comic Book Guy question – but do I gather that if someone swallows a tiny bit of zombie blood they won’t turn into one of the undead? There was a lot of it being sprayed around this episode [Season Three, Episode 6, Hounded].
A: Yeah, people to a certain extent think of zombie blood as being like the blood from Alien. You know, in the Alien movies it’s like, “Oh god, if it touches you, you explode!” or whatever. Whatever it is that turns these people into zombies is in them already. So the idea of getting zombie blood on your face, which happens all the time, and it turning you into a zombie is something that’s just not the case.
Now, that doesn’t make the zombie bite any less lethal. You know, breaking the skin, having that kind of contact with the toxicity that zombie mouths would have, would be something that causes an infection that definitely would lead to your death and then the thing that’s already in you would turn you into a zombie. So there is a science to this, to a certain extent.
Q: Although, to be clear, you are not technically a scientist.
A: No. No, no, no. But I know about everything that scientists know, I’m pretty certain! But anyway, zombie blood is not quite as deadly as a lot of people think. I wouldn’t drink it in high volumes, though.
- Robert Kirkman, interview with Entertainment Weekly
We know everyone is infected already, but it is possible that someone is immune. With the world ending there aren't many doctors to consult on the subject.
In the TV show version, it is possible Jenner told Rick more than everyone is infected. He could have also said "but your son is immune." Rick wouldn't want to announce that. People like the Governor would cut Carl up to try and find a cure.