American duck sauce and traditional duck sauce stem from the same Chinese sauce: plum sauce. However, most American duck sauces use apricots instead of plums.
The jelly-like American duck sauce was originally sweet and sour sauce. However, the chef was the only one who knew recipes in a Chinese restaurant in the early days of American-Chinese cuisine. When the chef was sick and unable to make the sauce, plum sauce was substituted for use with egg rolls. Early Chinese immigrants could not easily translate plum sauce, and so they decided to associate it with the duck that it is usually served with. The trend of traditional plum sauce being called duck sauce continues today.
Traditional duck sauce has two forms: plum sauce made from dried plums, and pickled plums mixed with brown beans. The latter is mostly used on pork ribs, but is also used on fish.