OE is the original. It’s Kodi with a bare minimum OS so that it can run on its own on a device. Due to some differences, most developers from OE left to start LE. Their mandate is to have a planned and regular upgrading schedule for LE. The creator and main developer is still at OE.
There’s also OSMC, which is a more fledged Kodi installation. The difference being it has a specific Debian disto as the OS for Kodi to run on.
LibreELEC is a fork which means they took the OpenELEC code and used it as a starting point for their own project. So to answer your question, it is mostly identical as far as the end-user is concerned.
A key difference right now is that LibreELEC is active and up to date. OpenELEC had no development for several months. I see some development activity lately but with no announcements from the developer it’s hard to know what the future plans are.
If you want to be on the latest version of Kodi then you should use LibreELEC. It is easy to migrate.