So will it be correct to classify PRNGs as KDFs?
There are two important differences:
Removal of any correlations in the output bits that could help compromise other algorithms that use the key. Cryptographic PRNGs satisfy this by default, but for example LFSR based algorithms do not.
In case the input is a password, it is desirable that the KDF takes a ...
While PRNGs are not exactly KDFs, there are several constructions of KDFs from PRNGs (actually PRFs, but they are equivalent). This is similar to how (symmetric) encryption is not the same as a PRG, but it is simple to build symmetric encryption from a PRG.
To read more about this, see NIST 800-108. There are three constructions listed from arbitrary PRFs.