Folia is probably the most interesting on this list - it's a mod by the makers of PaperMC to parallelize Java Edition while still maintaining a working survival experience. It's best known for powering 2b2t, a anarchy server with a current player count of 633 on a single survival world, with the world being roughly as old as Minecraft multiplayer itself (servers that are effectively multiple servers chained together have hit CCUs of 216k).
Bukkit is the name of the API for the server software Craftbukkit. Bukkit itself is not server software. Plugins targeting the Bukkit API can run on Craftbukkit, Spigot, Paper, etc. Plugins targeting Spigot API only run on forks of Spigot (if they use the parts of Spigot API that are not in Bukkit), but not Craftbukkit.
I was researching Java edition specifically, however among the ones linked below, at least one (Nukkit) has a Bedrock (C++) edition.
Many of these are related, e.g. Paper is based on Spigot which in turn is based on Bukkit.
Paper seems to be the most widely used currently.
Paper https://papermc.io/
Spigot https://www.spigotmc.org/
Bukkit https://dev.bukkit.org/
Nukkit https://cloudburstmc.org/articles/
Folia (mod for Paper) https://github.com/PaperMC/Folia
PaperBin (mod for Paper) https://github.com/x4e/PaperBin