Nil or Zero

The number 0 can be called either 'zero' or 'nil'

As far as I know, nil is only used when talking sport score and then you use zero for all other purposes. Is that right? And is there any diffrence between them? Can you use nil instead of zero if you want and otherwise?

Americans wouldn't say "nil" for sports, though we may say "the chances of that happening are nil."

We often say "oh" for zero. They're leading six-oh means the score is 6 to 0.