So if I have 1 blue A board and a bunch of various blue B boards I could play all of the games with just the one A board correct? (Not all at once of course)
yep. You can also play green ones. Orange and grey ones both have difference motherboard configurations and will only play games from their region. The motherboard will only save setting from one game at a time though. You will have to change your settings every time you swap a game or just leave them default.
Edit: you can also play some yellow rental ones also. Yellow was used in all regions but is pretty rare. You would just need to know what region the particular board was from.