I gave them my link, but at checkout there is a different coupon. Do I still get credit?

Yes. A checkout takes one discount, and if there is a site-wide sale on, they get whichever is bigger: your 20% or the sale. Your credit does not depend on which one won. If they arrived through your link or typed your code, the sale is yours.

Your commission does not shrink either

You earn on the list price, not on what they paid. A deeper sale for them is not a smaller commission for you.

The one case that is not yours

If no link brought them and they typed somebody else's ambassador code at checkout, that person is credited. A code can only be typed when no link is already applied, so the two never compete.