A very good question. The identification of Greater and Lesser Scaup is not an exact science.
There are, however, some characteristics which can help.
Size: Greater Scaup measure 16 – 20 inches in length while Lesser Scaup measure 15 – 18 inches. I have seen stuffed examples side by side and the difference is quite evident.
Head gloss: This tends to be green in Greater and purple in Lesser.
Head shape: The crown of the Greater Scaup is generally less puffed up than in Lesser Scaup.
Time of year and habitat: Wintering scaups are usually (but not always) Greater, while in summer they are usually Lesser. Greater Scaup often gather in large “rafts” in deep water while Lesser Scaups are usually in smaller groups in shallower water.
The best way to distinguish the two is to see them flying. The wing stripe in the Greater extends well beyond the bend of the wing but stops at the bend in Lesser. This isn’t much help because Scaup spend most of their time on the water, not flying.
The origin of the name scaup may stem from the bird’s preference for feeding on scalp—the Scottish word for clams, oysters, and mussels; however, some credit it to the female’s discordant scaup call as the name’s source.