No, I understand that. It's a terminology problem. I've been using PoW to refer to the hash whether it is valid or not. I see now that PoW is defined as only the hash that has the number of leading zero bits.
Well, yeah. Technically the greatest possible target, or a difficulty of 1 is a hash that is smaller than 0x00000000FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF. PoW is a concept whereby we measure the estimated work done to do something, where in this case would be a hash that meets the specific requirement.
I'm not sure I understand the difference between leading zeroes and difficulty though. People throw around the term difficulty rather loosely as though it is a euphemism. I prefer concrete terms.
Actually, difficulty is just a representation of the target. It is far easier to say a number than to actually say the target. I find it easier to describe target with the number of zeros, because a the maximum target (and lowest difficulty) has 8 zeros and loads of people have no idea what it means when I talk about target. Leading zeros is a dumb down concept that is easier to describe to most people. The more correct method of describing a target is to compare the hash to a 256bit number, and it's validity is determined by comparing the hash and the target, where the hash has to be smaller than the target to be valid.
I didn't really refer to your terminology but your understanding of how a pool function. If you can understand how a pool works, either through looking at stratum documentation or a pool's code, then it shouldn't be difficult to understand what's going on.