Have we got any eggs?
vs
Have we got any egg?
What is the difference between these two sentences in terms of meaning?
"Eggs" is countable and means those oval things that are laid by birds.
"Egg" isn't countable. It normally wouldn't make sense to say "egg" as eggs themselves are countable, but you could say "have we got any egg" if you were in a restaurant kitchen that used powdered or liquid egg rather than individual shelled eggs.