There's a pretty big difference, actually.
Rhythmic floors are much thinner with no springs at all. It's 13 meters by 13 meters within the boundaries. 1 meter safety border.
Artistic floors are thick and plush. It's 12 meters by 12 meters within the boundaries. 1 meter safety border.
The color of the floor doesn't actually matter--blue, red, white, it's all good. It's most likely because of the big gymnastic brands manufacturing a certain color in the beginning and it just caught on. If you look online, you can find floors in green, yellow, and black.
The floors are different because of what the gymnasts need out of them. Rhythmic gymnasts don't want springs--it's harder to balance and hard to pivot. Artistic gymnasts need the spring for tumbling and power not to mention not killing their knees after a tumbling pass.
So, to sum up, artistic floors you sink into a little and they're cushiony and springy. Rhythmic ones are a little bigger, textured and thin so you can feel the wood under it.