'Undulata Albomarginata' is the green one with a white margin that your grandmother grew. It's been around for a long time. Most of us have at least one plant and I'm no exception. I've got four and I've got them for the duration as the roots are mired into the Linden tree roots. This is an old variety, but it is still very nice and it blooms well. Please feel free to share your photos of this hosta.
I have had these plants for several years now, and it seems the white margins are beginning to fade to green. This Hosta does very well in my warm climate, but I did prefer the white margins.
I think the "Undulatas" are known for greening up during the season. It likely happens more with the white centred one. It doesn't happen much in my zone, but is likely to be noticed more in yours.