The red trailed one or one very similar was seen on the Style and Design website with an attribution of possibly STevens and Williams or Orrefors if I recall. I'm not sure how they got their attribution but I think your labelled one clinched it as RB.
I'm not sure what the significance is of the different labels but I would think the trailed one would be an earlier piece. I wonder if they, or at least some of them, fall under Royal Brierley and not Royal Brierley Studio. It's quite confusing from what I recall reading, there were two 'Studios' somehow. I'll need to go and look the info up again but I think it is in CH 20th Century British Glass?