The different types of messaging (and their corresponding NIPs) are explained well on the nostr:npub1tm99pgz2lth724jeld6gzz6zv48zy6xp4n9xu5uqrwvx9km54qaqkkxn72 GitHub.

The anonymous button in Amethyst makes it a gift-wrapped DM if I’m not mistaken, which is more secure mainly because it doesn’t have metadata leakage. 

https://github.com/0xchat-app