Actually there is no real way to tell those 2 appart.
The only time we saw hourais was in PCB, shangai spell was easy,normal and hard while hourai was lunatic. Difference? nope, the sprite was the same. And that sprite is the same used for all the dolls but the red-haired dutch ones. After that we all see alice using the same doll over and over, until SA where marisa uses a few red dolls, adding something to this alice seems to dress the dolls like her (well if you go by 12.3).
But if you look back in time it used to be red for shangai and blue for hourai. Mostly because of 2 things (probably), 1 being that shangai is in china, and china's flag is red. And the other one, and most important, is that in marisa stole the precious thing, when you see the dolls, shangai is the red one.
So, shangai? hourai? well right now everyone calls shangai to the blue one and hourai... who knows. People right now like to call them shangai. For me this are hourais while the red ones are shangais.