it is interesting to see how people use them.
we say "equal opportunity" in terms of treating people without discrimination, but we don't say "equal chance" in this context. is it because "opportunity" can be offered by man whereas "chance" is random?
is it why we say "they have an equal chance of winning the game" instead of "equal opportunity of winning the game?"

but sometimes both are interchangable.

there must be a subtle difference between the two, or there would be a need for both of them to exist at the same time.

what is it?

It seems to me that you already have quite a good grasp of the differences here.

Best wishes, Clive