Source? Afaik, coconut milk and soy milk have not only been made for centuries, but also called something like “milk” where they were consumed (e.g. India, China, Thailand, etc.)
ETA: The Mahābhārata, a book dating back to 400BCE, refers to making rice milk. So...
Different how? It's definitely no less "milk" than cow's or sheep's or goat's milk. As a substance it's definitely as much "milk" as it can possibly be.