Shangai and Hourai are supposed to look the same BUT due shangai being in Imperisable night and using a red dress in that THEN Shangai = Red Hourai = Blue
I don't think that really matters at this point, since based on the canon, Alice has multiple Shanghai's at her disposal and lots of other dolls.
However, the blue doll with the red bow is often associated to Shanghai now in fanon and in almost all instances in doujins with Alice you'll see that particular doll being refered to as Shanghai.
So nowadays, Hourai is considered the one in red with the bunny eared bow(like Tsukasa from Lucky Star has). Although depictions of that specific doll can change (I've seen pics of her with the kind of bonnet that Remilia wears).
Well looking through the Shanghai tag here on danbooru that's certainly the trend.
But seriously, most touhou fans associate Shanghai with the blue dress and red ribbon. She's shown with them a lot more than with the red dress version.
Most people can at least agree on the fact that the doll we usually see hanging around Alice is in fact a Shanghai doll right? Well that doll is often portrayed as being that blue dress one.
There's no difference to see in this pic, they're all supposed to be Shanghai dolls. Hourai dolls nowadays (defined by fanon mostly) is usually seen as a doll with a rabbit ears like bow and a red dress or a puffy hat. Sometimes associated to the hanged doll pictures you can sometimes see (although Shanghai does that too in the fanon thanks to SWR and IaMP).
I'll add however that it varies a lot (like Momizi's look or Koakuma's personnality) because there isn't a lot to go by and the character has been mostly defined by fanon (like Sakuya, who is actually supposed to be a pretty airheaded girl...well fanon said screw that).
