What is the definition of genuine entanglement?

I can't seem to find a definition for genuine entanglement but it is being used in an article I'm reading and the references inside but I'm unable to find the precise definition.

One thing I was able to get to the bottom of is "So far, genuine multipartite entangled (GME) states in the form of Greenberger-HorneZeilinger (GHZ) states..", but I do not know what about the GHZ states makes them "genuinely entangled".

Also the way it comes up is "genuine multipartite entanglement", which begs the questions (after what is genuine entanglement) why does it only come up in multipartite schemes ($$n>2$$)?

Cross-posted on physics.SE

• I'm voting to close this question as off-topic because it was also asked on Physics SE and it is discussed there. Here is a link: physics.stackexchange.com/questions/543411/… Apr 12 '20 at 22:39
• @MartinVesely see this discussion on meta about cross-posting (you might want to argue about whether we should not allow it?)
– glS
Apr 13 '20 at 14:59
• I think it should be allowed just because of the difference in the overlap of people. On Physics stack more often people will give purely physically motivated answers/references while here people will more likely give a quantum info motivated answer/reference. Apr 13 '20 at 18:16
• I agree, I retracted my close vote. Apr 13 '20 at 18:18