Now-a-days with the new fashionable pajamas it's hard to tell the difference.

Women in Russia like dress up even when they go shopping.

Not likely.

When I lived in Shanghai, I also noticed many people would wear pajamas to go to supermarket. The first time I saw it, I was a bit shocked. Haha. But gradually I was used to it. However, for me, I would never wear a pajama to do shopping or go out since I don't think it is appropriate. Here in Chengdu, I barely see people wear pajamas to go shopping or go to supermarket. 

No, not here in New England. Not for shopping, not even in a supermarket. I won't say it couldn't happen, I just don't remember it. If the pajamas are reasonably modest it wouldn't be a problem. But it would be sloppy, not fashionable.

I am surprised by the comment about Atlanta.