If you want to amend an existing Contract or Agreement, you can put a Deed of Variation in black & white. It will give the parties a binding record of the variation so there's no misunderstanding about the new terms.
The word used to describe a change to a contract or agreement is usually a "variation", "amendment" or "change". Or, if something new is added, an "addendum". Hence, a Deed of Variation is also often referred to as a Deed of Amendment and or an Addendum? There is no difference between these documents as these terms, or descriptions for the agreement, are used interchangeably.
The correct way to amend an agreement is to ensure the amendment accords with the requirements of the initial agreement. And, you will find that most agreements contain an "entire agreement" clause. It usually says something like, "This document constitutes the entire Agreement between the parties and no other documents will have any force or effect."
Therefore, you need to make sure the amending agreement satisfies the requirements of the initial agreement, in order for it to be effective. The initial agreement will likely contain a clause that says, "This Agreement may only be amended by a further written agreement signed by all parties to this document."
A formal Deed of Variation will satisfy the requirements for amending (or varying) most Agreements, since it is in writing and it is signed by all the parties to the initial Agreement. Furthermore, because it is a "deed" it will be binding even if the parties don't exchange consideration (or benefits). Whereas, a regular agreement, that is not a so-called "deed" will likely require that each party receives a benefit in order for it to be binding and legally enforceable.