The question lists them in ascending order of player level (descending order of speed). Blue is the fastest, and is recommended for beginners; the "double–yellow dot" ball was introduced in 2000 and is now the competition standard. There is also an "orange dot" ball, for use at high altitudes; this is even slower than the double-yellow.
Some sources describe a green-dot ball, which is the equivalent of the white (slow), and a red, which is between the blue and the green (or white). These appear to be older standards - I'm guessing that the red- and green-dot balls were replaced by the white.
Some manufacturers use a different method of grading balls. For example, Dunlop offers the Pro as the equivalent of the double-yellow-dot; the Competition is the equivalent of the single-yellow-dot, and gives 110% as much bounce as the Pro; the white- and blue-dot balls are matched by the Progress (120% of Pro bounce) and the Intro (140%).
© Macclesfield Quiz League 2016