Gotta somewhat disagree here. The only thing internal to the Amiga is the ability to synchronize to external sync provided by the genlock. The actual overlay is done in the genlock.
Genlocking is something that the Amiga can do all by itself, it only is the process of synchronising to an external clock.
Just because someone used the word genlock when marketing an external peripheral doesn't change that. They could have called it a video thingy.
At which point you'd say that the video thingy plugs into the amiga and allows it to genlock to an external video signal and the video thingy then mixes between the amigas output and the external video signal, based on the signal generated by the amiga.
Nobody is going to call it a video thingy though, they are going to call it a genlock. So if someone (like the OP) asks "what is an amiga genlock?" the answer is: it's a video mixer and slave sync generator that allows the amiga to genlock to the external video source.
In the real word genlock is a verb, not a noun.
So equipment is genlocked if it's synchronised to an external clock.
Equipment genlocks to an external clock.
It's unlikely the incorrect usage of the word genlock is going to disappear, so I'm not going to keep arguing the point. You'll either be educated, or you won't. I can't do anymore