What ever the name says, it isn't paper white. Actually, I think there is little difference, the difference is the light, which makes the PaperWhite look whiter in normal light and enables reading in dim conditions.

Perhaps some people read significantly more indoors or shade than direct sunlight

The grey background doesn't make it any harder to read. It's just less bright.

The Paperwhite is called that because it has background lighting via weak LEDs.