Hash functions and PRNGs are closely related, they share many properties and they can be built from the same algorithmic components, so for many kinds of PRNGs there are corresponding kinds of hash functions and vice-versa.

Nevertheless, the purposes of hash functions and PRNGs are different and complementary.

A PRNG receives a short fixed-length value (the seed) and it expands it into a long pseudo-random sequence of arbitrary length.

A hash function receives a long input sequence of arbitrary length and it generates a short fixed-length pseudo-random value.

Good PRNGs are injective functions and good hash functions are surjective functions.

Normally the design methods for PRNGs and for hash functions should be presented together, because it is easy to interconvert algorithms for one of them with algorithms for the other. For instance, given a good hash function one could make a PRNG by computing the hashes of a sequence of numbers or the hashes of a sequence of strings of increasing length, and given a good PRNG one could make a hash function by accumulating somehow the input into a PRNG seed and taking the first generated number, or better by using input chunks as seeds and then accumulating the first generated numbers into a single value.

However for a successful conversion between PRNG and hash function algorithms, the source algorithm may have have to be overdesigned, to guarantee good enough properties even after the conversion.

When an algorithm is designed directly as a hash function or as a PRNG, with clearly specified requirements, it can be designed only as good as strictly necessary, enabling thus a better performance.