The word "eat" has a more general meaning, we can eat all kinds of food. The word "nosh" is usually referred to snacks and to light food.

The verb 'to eat' is *much* more common than 'to nosh'. To be honest, I did not know the exact meaning of 'nosh' until I read here comment above. 'To nosh' is possibly from Yiddish but I don't know. Yiddish is a European Germanic language spoken mostly within the Jewish culture.