The following community FAQ is very old and the examples are out of date, but the concepts and terminology are still current and should help. The topic title is a clickable link.
Groovy is a programming language, like Java, Lua, Python, PHP, etc. It is not a SmartThings construct, it’s just the language That the original smartthings developers chose for their platform. However, smartthings is in the middle of a major architecture change, and support for the free groovy cloud from smartthings will be discontinued soon.
The new equivalent of device type handlers are “edge drivers“ which are written in Lua and will run on the smartthings/Aeotec hub.
Some power users may choose to continue using groovy and they can, but they will have to host it themselves and then communicate with their smartthings account through the API.
Other power users have chosen to go to a competing hub, Hubitat, which also uses the groovy language but runs everything locally, no cloud.