Waiver and release are two law terms. They both deal with waiving rights and privileges. A waiver will get of a person's rights in the event of a circumstance occurring. For example, if a person is having a pool party, they could make the guests sign a waiver that takes away their right to sue in the event something happens at the party. A release is normally an exchange of ownership of rights between two parties.
For instance, if John is selling his car to Mark, he could sign a release form, releasing the ownership of his car to Mark.
The main difference between waiver and release is how they are used. These are law terms that can be applied to different things that may be related to the law. When you say waiver, this means that you are abandoning a right or a privilege. There are some people who say that this can be similar to forfeiting something.
When you say release, this means that whatever responsibility that a person may have, the person will be released from it due to various reasons. For example, a person may be released from debt the moment that the person has died. It is important to know the difference so that you will know how to use the two.