Korean corydalis is a small perennial native to northeastern Asia that grows in open woods and along woodland edges. Its blue, violet-tinged, or white flowers have a long extension at the back that holds nectar, and the leaflike part just below each flower is deeply divided. It is not native to the United States.
Spring corydalis grows in New England gardens and has also naturalized there. Its spurred purple flowers can look similar; a flower photo alone may not reliably separate the two, so check the plant label or other parts before naming it.
Why they get mixed upBoth are low spring plants with divided leaves and spurred flowers.