How are you differentiating nusach from melodies?
Would you call the nusach for Shabbos chazaras hashatz (for example) a song? I would not, although I’m not familiar enough with musical lexicon to articulate precisely why.
A common (not necessarily exclusive) characteristic of a melody (song) as opposed to nusach is that it generally is imported from a different context (tish, kumzitz, recording) whereas nusach is exclusive to tefilla.
Also, nusach generally stays constant from tefilla to tefilla (of the same type), while melodies are more interchangeable. I’m sure there are others.