Project Website: https://simplex.chat/
SimpleX Chat is unique for a number of reasons, most of which require a technical background to understand and are rather complicated. As written on the project's website, “Other apps have user IDs: Signal, Matrix, Session, Briar, Jami, Cwtch, etc. SimpleX does not, not even random numbers. This radically improves your privacy.” It is available for Android and IOS, and text-based clients are available for Linux, Mac, and Windows.
Due to the lack of user ID's, automatic discovery is not possible. Contacts must be added by scanning a QR code or sharing a string of characters. This can be done over less secure channels if need be, according to the project's website. This has not been researched by the author of this page.
SimpleX uses the project's server by default. However, one can host an instance of the program for even greater privacy and reliability. See the instructions here.