I guess I need to modify my comment, since "waive" is also transitive and takes an object (e.g., waiving a "claim"). Duh. The distinction I was trying to make should remain the same, however. As "anon" puts it more succinctly, a waiving party is forgoing a right or claim against another party, usually before such a claim has actually arisen. In contrast, a party that has been released from liability can raise the release as a defense if the waiving party tries to pursue a claim against the released party if the basis for such a claim ultimately arises. Both a waiver and a release would logically describe the rights, claims or liabilities in question, so the scope of a waiver and a release should normally be the same. But, even if I do not expressly "waive" my rights or claims against the other party, I still should not prevail if there is a clause under which I released that party from such claims, and that release remains binding on me.

I think I "waive" the right to pursue a claim. In contrast, I think I "release" someone else from liability. As a practical matter, I think the result is the same, no liability. But I think the possible nuance is that one is transitive (release, which takes an object) and the other is intransitive (waive, which does not take an object). And I think both could be used together: I "waive" any potential claim against you for payment, and I "release" you from any liability you might have to me to make such payment. I think I have even seen some legal documents that say "waiver and release," to cover both bases.