They look the same.
Sauce vs the Relish
Both dishes start with fresh (usually) cranberries and some sugar, but here’s where they differ after starting with those 2 main ingredients:
Cranberry Sauce: has water or orange juice as 3rd and final ingredient. Cranberry sauce is all sweetness.
Cranberry Relish: is more sour, spicy and has ingredients like onions, horse radish, vinegar etc. More like a typical relish.
Both dishes can be varied quite a lot but the main differences generally remain:
Sauce: Sweet (how to make it thick)
Relish: Sweet + other flavors and onions (and all that).
Hope this helps sort it all out.