Is the bits field a unique representation of the target?
In short: no, the nBits encoding is not unique (there may be multiple 32-bit values that correspond to the same 256-bit target), but the nBits value as required by the network consensus rules is unique.

The reason for that is that all calculations happen on the target, which is then converted (using a deterministic algorithm) into nBits format. That nBits value is then required to match the value in the block header.