Well, I'm sure Angie will have perfect answer, I can only partially answer this. I hope I don't embarrass myself!
I believe the following: couture and haute couture is the same. Some designers show both haute couture and pret-a-porter lines (separately), some specialize in one type, some have multiple lines of one type and so on and some even have lower cost lines - so-called bridge line. Pret-a-porter ( well at least most of it) will arrive in fancy stores as shown on the runway and you can buy it there.
Haute couture is not available in stores and can only be custom made for you upon your request. Technically I think BR is not not pret-a-porter, although any company can have a fashion show and call it that.
And I've learned from a great book ( "Pocket Stylist") that in general fashion lines can be divided into following groups based on price/quality ( I'm omitting the lowest since I don't know how to classify them):
Better Lines ( e.g BR, J Crew, Zara etc)
Bridge (Theory, Elie Tahari, Nanette Lepore), very often also called Contemporary.
Designer (self-explanatory).
Some designers will have both bridge and designer lines, e.g. Marc Jacobs has his namesake designer line and also a bridge line called ' Marc by Marc Jacobs'.
