The question concerns agreements in general; someone with legal skills should be able to answer the question...?Do you have any more context, Acgsg? I don't want to spend time answering you and then find you were thinking of the words in different linguistic circumstances.
Thanks a lot !I'm glad I asked for clarification, for it helps greatly to know that the context is formal and legal.
Here is an official EU document illustrating the difference:
1. What is an amendment to the agreement?
An amendment to the agreement represents a substantial change to the grant agreement originally approved by the European Commission. This substantial change must be included in a written additional agreement, which has to be approved by the European Commission.
So it seems that here, at least, an amendment is a general word for a change, which is then formalised into a written additional agreement.
The need for a definition in this case suggests that there is no general convention about the difference between the two, so perhaps the legal systems of different English-speaking countries treat the words in different ways. This would make a helpful general answer impossible.