How deos Apple replace iPod touches?

They replace it with the equivalent model.

 

Not always true. My friend bought a refurbished 1st gen a few weeks ago and the wifi didn't work. He sent it back to Apple, and instead they sent him a brand new 2nd gen. I'm guessing it was an exception.

But, in the OPs case, I'm not even sure they will replace it. They might just clear out the dust from under the screen.

 

It's a simple process to take the screen out. And no do not even think about trying it because you need the right tools.
Apple will replace the screen for you. This is not garunteed because I have heard my cousin, he works at the store, tell me that they become lazy so sometimes they change the whole product and throw this out. Don't rely on that, i think it's false.

Anyhow, they will most likely pop the screen out and change it.

 

Nope. I've had two iPod touches replaced for dust under the screen, and that wasn't even in an Apple Store, it was sent to the proper technicians themselves and went through all the normal tests - it was, according to Apple's service page, tested on for no less than four days; more than enough time to take the screen out and put a new one in, yet both times I received a different unit back.
Not to mention the countless iPhone owners that got replacements for the exact same problem. I'd say it's more likely they'd get a replacement.

And to answer the initial question, it's a 99% chance you'll get the same model as a replacement. The only way I can see you getting a 2G is if they are unable to find any refurb 1Gs.

 

I doubt Apple actually bothers expending the resources to make a distinction between something that can be quickly repaired versus some thing that would be quicker to simply replace. Simply making that determination, in some cases, would ultimately result in a slower turnaround time for the customer.

Rather, in all likelihood, Apple has a streamlined procedure for dealing with every returned product:
1) Confirm whether or not the product is still eligible for warranty support. (Evidence of moisture? Evidence of blunt force trauma? Evidence of unauthorized tampering? AppleCare purcahsed? Expiry date of warranty exceeded?) If not, return it to the customer.

2) Confirm whether the product is actually malfunctioning in the way described by the customer. If not, return it to the customer.

3) If we made it this far, grab a replacement off the "refurbished product" pile and ship it back to the customer right away.

4) Place the old unit onto the "needs repairs" pile. It will eventually work its way through the system and end up either discarded, or on the "refurbished product" pile ready for redistribution.