Each hash a miner does is using a different blob of data.  A single change in a single bit will produce a completely different hash, with no deterministic way to know how it will change.  To prevent miners from repeating work, pools take a template of work, and increment a pool-side counter for each miner's work.  This means the template each miner receives is slightly different, so that they will produce completely different hash results.  Miners then take this template and have three values they can change:

1) ExtraNonce - A piece of the coinbase (payment transaction) that allows for a miner to increment a counter.  Most pools use 4-bytes for this value, meaning ~4.2 billion possible increments.
2) Nonce - Another 4-byte counter, this is part of the block header.  It has ~4.2 billion possible values as well.  You can use up ~4.2 billion nonces (~4.2 Gigahashes), then increment the ExtraNonce by 1, which allows you to try all 4.2 billion Nonce values again.
3) nTime - This is a timestamp part of the block header.  It *can* be altered within certain limits.  Each change in this would be another 4.2b x 4.2b possible hash results.  Most miners do not increment nTime anymore because there is no reason to alter timestamps with how much work can be generated by default.


By changing a single bit on any of those 3, you get a completely different hash.  There is also the pool side counter for each miner so there is no overlap, and then each pool has different payout addresses so no pool has overlapping hashes either.