It's basically a way to differentiate between the two forms of COPD - chronic bronchitis and emphysema (though my understanding is they're treated almost exactly the same clinically).
Pink puffer = emphysema --> basically they're putting a lot of their accessory muscles to use during exhalation so they'll generally be blowing off a lot of CO2/hyperventilating. Hence they'll often have a reddish face and breathing hard. They also tend to be a thinner than in chronic bronchitis.
Blue Bloaters = chronic bronchitis --> basically refers to the fact that you have a bit of cyanosis due to increased PCO2 in CB because the mucus plugs make it hard to blow off extra CO2. In addition they tend to be obese hence "bloater", though I'm not actually sure of the pathophys behind that.