Snuffy has it almost right...Lady Raglan first applied the term "Green Man" to "foliate head" carvings in church architecture. But she did not actually coin it, Wikipedia notwithstanding. She took the name from a common English name for a pub or inn.

As Raglan herself says,

"I should like to remind you that there is an extraordinary number of 'Green Man' inns all over the country. I have noticed them particularly in East Anglia."

What she was doing in her articles was to argue for historical continuity between "foliate head" carvings and more contemporary phenomena, in particular Jack-in-the-Green enactments at May time, and the common pub name The Green Man.

Many Green Man inns featured signs illustrating a character who looks more like Jack in the Green than like a foliate head.

theleveller may be right or wrong about the Green Man and Jack-in-the-Green being different, depending on whether we accept or reject Raglan's idea. If we reject it, then "foliate head" carvings and "Jack in the Green" enactments are indeed totally different phenomena...and neither one is the same as "The Green Man," which is a traditional name for inns and pubs, and a traditional green-clad character on inn signs. If we accept Raglan's idea, then they are all manifestations of the same tradition.

Interestingly, if we were to partially accept Raglan, it would be easier to accept that "The Green Man" (pub character) and "Jack in the Green" (chimney-sweeper's mayday enactment) were the same; they look very similar, and are also roughly contemporary. "Foliate Head" carvings are from a totally different time period, and look very different from the other two traditions. So I would argue that it's possible that Jack-in-the-Green IS the Green Man, but that the church carvings are something else again.

leeneia's idea is interesting, and applies well to some versions of the foliate head, but not very well to others. I think it was a symbol whose meaning changed over time, and also one that different carvers used to express different ideas.