All of CalyxOS, LineageOS, LineageOS for microG, GrapheneOS and /e/ are Android distributions (based on the open-source part of Android, with some modifications and additions)
Purism (brand name) Librem 5 (model name) is an opensource smartphones that reduces black boxes to closed areas, while on most smartphones black boxes like modem share RAM access, using a brand new GNU/Linux (so not Android) smartphone OS.
microG is fundamentally simply an opensource Android app, that replaces some small parts of Google Services (which are very big unauditable closed-source Android apps), so apps requiring Google Services may have a chance to work without Google services. However microG requires a bit more permissions than a standard app, that's why there needs to be a "LineageOS for miroG" to support microG.
Now, between CalyxOS, /e/, LineageOS, and GrapheneOS:
- LineageOS targets devices support. LineageOS supports many devices officially, and provides infrastructure to support many more unofficially. They also include many features, but it doesn't feel like they have a specific orientation, and they are happy to integrate with Google apps. They are the very core of Android community original development.
- GrapheneOS is security first and foremost, no matter the cost to usability (their philosophy there does seem to evolve to open to more users recently). They do (great) security original development.
- /e/ is market first. They focus on having the best experience to the user, and try to reach as many users as possible. They have very little original development, their value is mostly in communication, and providing a "cloud" account.
- CalyxOS is targeting a good private user-experience. This goes both by having good usable defaults, and filling gaps. They have nice original developments in making Google-less more usable.