All of these are derivates of the base android operating system. They are basically attempts to reconstruct functionality that is removed when you get rid of all of the google software from android. Several offer increased privacy, while others offer better security. r/degoogle has a fairly decent wiki on the topic, as well as r/privacy. The short version is that they are freely made products, and come with all of the risks associated with community and open source products, but can potentially have better security and privacy. The differences between the OSs are generally due to goals, some, like grapheneOS want to be as secure as possible, at the expense of other features. Some, like lineageOS are mostly about having an open source phone environment that is actually usable and friendly. To pick one you basically need to decide what you want out of installing a new is on your phone, and what you are willing to sacrifice for that.

Uneasy laughter

I should stop rooting