Amnesty means not paying for a crime.
The 'crime' in this case was crossing the border illegally.
The "deport them" crowd just wants to send them back across the border. That would be "amnesty", because it doesn't punish them for thier crime. (sending them back isn't punishing them for the crime, it's just stopping them from continuing the crime -- it's like if someone is siphoning your gas, and you make them stop but don't shoot them, you have given them "amnesty").
Bush wants to make them pay a fine. That's punishment for the crime. We can argue over what an appropriate payment is for the crime, but at least he's got a punishment in store for them.
Then, he wants to give them visas to stay here while they wait in line for citizenship. That's not amnesty, it's a visa program. Or you can say he's rewarding them for their illegal behavior.
Much like if you drive 90 mph in a 60 mph zone. You do it for 4 hours, and then a cop pulls you over, and gives you a ticket (if he didn't, it would be amnesty). But you've also BEEN REWARDED, because during that 4 hours you got a LOT further than those who drove 60. To be "fair", the cop should make you sit on the side of the road until enough time passed to make up for your speeding.
But the cop can't afford to do that, he's got a job. And it really wouldn't make sense to make you sit around, as "fair" as it would be. In the same way, it just doesn't make sense to send them home if we are going to let them back later.
So what about the billions of other people who would like to enter the US to work while they wait in line for citizenship, they don't get to enter and wait here. WHERE ARE THEIR VISAS?
Its a reward for jumping the border and the line. Clear and simple.