Bukkit was the server software for plugins that started everything many years ago. Some years later some guys forked Bukkit and started Spigot - an enhanced server software which supports Bukkit plugins but with better performance.
In 2014 the development of Bukkit stopped due to reasons. As Spigot was based on Bukkit the team of Spigot continued the development of Bukkit and are still updating it.
Meanwhile Bukkit is here only for compatibility reasons and because Spigot is based on it. Honestly I don't really know if there are still differences...
In general it's recommended to use Spigot. At Aternos we removed Bukkit itself last year and merged it with our Spigot category.
Last but not least there is Paper - a fork of Spigot with more performance optimizations.