What is the difference?

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Well in classful addressing you will treat IP Address strictly by the A,B,C,D class masks. So if you only use strictly Classful addressing then if you had the address

10.0.0.0

You would only have on available network as the subnet mask for class A is 255.0.0.0. However, if you use Classless addressing then you can really control the amount of networks you have per ip address. So if you had that address you can borrow "network" bits from any of the octets beyond the first one (well beyond what is normal for that class). So you could have the address 10.0.0.0 but use a subnet mask like 255.255.255.0 and now you can have a very large amount of networks. You could customize this even more. This is what is known as Variable Length Subnet Mask. Hope this helps.
-neural

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So I can set any subnet mask for any IP as long as it's private. This can't be done for Public addresses though, can it?

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Ok forget I asked that. I'm learning as I go here.

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