Will a case for iPhone 3G fit on a First Generation iPhone?

I want to buy a case from eBay but I don't know if it will fit.
The case just snaps onto the back

No it will not, the 1st gen is more square, the 3G is a different design.

I don't think so because I'm pretty sure the 3G is thinner then the original model.

Not properly. The 3G has a more curved back vs the iPhone's flat back.

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