I saw you ask this on the Devic thread. I held back on answering because I’ll be a little bit of an outsider answering. I don’t hold beliefs on this subject. But since you’re not getting answers so far I’ll try to help in the mean time and then hopefully some will speak for themselves.
I think some who say Gaia believe it will have a pivotal role to play in Earth 2.0 but only if they happen to believe in both of those things.
But for them and for others who believe in Gaia but not necessarily Earth 2.0, I think they are using the name Gaia to indicate they believe the planet is conscious and has an intelligence and will.
Among those who believe that, the specifics of how intelligent and how conscious seems to vary from a subconscious kind of intelligence to something more like a superintelligence or demigod compared to us. Not that subconscious is necessarily less intelligent, but less conscious deliberate or voluntary - acting upon a great deal of intelligence perhaps but not in a prefrontal cortex kind of way.
And others I believe use the term not to indicate a conscious planet but a planet that is due respect and care nonetheless.
And the lines between the planet being alive and being filled with life also vary among all these people.