I have no horse in this race and pardon my nitpicking but those two phrases are not equivalent.
For E2EE,you describe the base level capability: Secure message between two parties.
For Mixers, you describe an act that the capability of making money hard to trace enables: Money laundering. If you applied a similar argument to E2EE (as many have and will keep doing), encrypted communications are a way for people to do illegal things away from the eyes of the law. Trade illegal items, send banned/illegal/questionable content, etc.
From a pure capability standpoint, mixers, like E2EE, are a way to secure XYZ activity (Which happens to be money transfer) from prying eyes.
For E2EE,you describe the base level capability: Secure message between two parties.
For Mixers, you describe an act that the capability of making money hard to trace enables: Money laundering. If you applied a similar argument to E2EE (as many have and will keep doing), encrypted communications are a way for people to do illegal things away from the eyes of the law. Trade illegal items, send banned/illegal/questionable content, etc.
From a pure capability standpoint, mixers, like E2EE, are a way to secure XYZ activity (Which happens to be money transfer) from prying eyes.