Ok, that makes sense. Yes, I see chance as distinct from luck but they _can_ interchange too. Chance has a sense of “windfall” – a tree falling that you needed and now don’t have to cut.
Luck I associate with “just my luck” or “good luck / bad luck” or “lucky charms”.
The Chinese have whole complicated systems surrounding luck. It has a similar feel to me as Greek/Roman deities: Fortuna I think. (O Fortuna!)
I think of chance as equivalent to statistical probability as used in card games and statistics.
Astrology: “Today will be your lucky day”. Or what I often have heard, “Oh no, three bad things happened. Today isn’t my lucky day” and then they unconsciously do things to make their day worse, etc.