Red and sugar maple are different species. Generally, red has more vibrant, bolder figure, sugar is harder, more dense, and when highly figured, a little more subtle.
Fiddleback and tiger maple are just descriptions of that figure in either species.
I've been told that birdseye is the ends of the figure. In other words the board is cut the other direction and you're seeing the ends of the figure instead of the side.
That one, I'm not sure of.
This I know for sure..... I just finished the most difficult, beautifully figured stock in red maple. From now on..... I'll use sugar maple.