The American "Merriam Webster's Collegiate Dictionary" (10th ed.) somewhat limits 'carol'.
1. an old round dance with singing.
2. a song of joy or mirth.
3. a popular song or ballad of religious joy.

One must resort to the Oxford Dictionary for enlargement on 1., wherein is quoted from Caxton, 1483, under 1c, " Thassembles of martirs, the Countes of Confessours, the Carolles of Virgyns," and other quotations to encompass "song with a secular tune" (MacGrath, above).

The version in "Ancient English Christmas Carols" by Rickert seems to have originated with the Sloan MS in the British Museum, with spelling modernized (Masato, above).