A colour standardised in 1934, see notes on white and frost white.
Of Stone White no history is found.
Eggshell is meant as a representation of the average colour of a chicken egg. Chicken eggs may vary between pale brown and white, the colour is an average between the two.This is closer to white than pale brown, because more eggs are white.
In Interior design, the colour eggshell is commonly used when seeking a pale, warm, neutral, off-white colour.