So... Chance and luck are different things?
Of course! The word "chance" has gambling connotations, while the word "luck" is loaded with superstitious undertones :-) The only difference comes from the perspective of the person you ask.
More semantics than anything of substance. Luck is the lay man's term for probability and has nothing to do with superstition. And chance, well, that's just luck!
Semantics or not, some of us prefer to use technically correct terms for things.