The whole point of one way hashes is to provide a function where it is impossible to determine the input given the output. While any given input will always have the exact same output every time, a one way hash does not guarantee that given all possible inputs there will be an equal number of outputs. Thus, the strings produced are not necessarily unique.

For point of illustration, consider f(x) = 1. This is a one way hash. While not a very useful one, it does illustrate that not all values produced are unique.