Well, there both from the same Slavic root (probably Polish nuda 'boredom'): nudnik is a nomen agentis, 'one who bores, or bothers' from nudyen 'to bore, pester' (the digraph {dy} in Yiddish indicates a palatalized consonant). The suffix -nik also comes from Slavic, rather than the Germanic base of Yiddish. The verb nudzh (also nudge) is used as a noun also, probably under English influence: words changing syntactic categories without derivitive morphology, i.e., no suffixes needed. You see the same thing with the English noun schmier (for cream cheeese, etc.) derived from the Yiddish verb shmiren 'to smear'. The PIE root *n@u-ti- also gives English need and German Not.

So, what's the diff between 'em. Not much, I'd say.