The bits field is the compact representation of the target.

Example:

bits: 1d00ffff
target: 00ffff0000000000000000000000000000000000000000000000000000

bits: 1cfff00
target: ffff0000000000000000000000000000000000000000000000000000

But these two actually represent the same number.

int(target) -> 26959535291011309493156476344723991336010898738574164086137773096960 for both of the above targets.

What (if anything) makes bits a unique representation of the target?

Clarification:

In regular interactions with numbers, this kind of thing doesn't really matter, as a few leading zeros don't affect how we interpret the number. However, in Bitcoin, the bits field is used as part of the hash of the block. Therefore, a different bits representation would produce a different hash of the block.