If my memory serves me right, counterpoint isn't always a canon - a canon is specifically the same melody (though may be different words, if we are talking in terms of songs) started at a different point in the song. If the same words are sung, then it is a round, like Frere Jaques.
Counterpoint music may have different melodies for each part, which the Doctor Horrible musical does, but each of those sections and voices come together melodically.
from Wiki:
Quote:
In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm, and interdependent in harmony. It has been most commonly identified in Western music, developing strongly in the Renaissance, and also dominant in much of the common practice period, especially in Baroque music.
Rose Red (if you can find a good recording of it, someone seems to have recorded a recent and not very good version and I can't google it for her name being everywhere, and somehow the lyrics of this traditional song being attributed to her) is a good example. It starts of as a round canon, then two or three extra voices join in with separate verses to form a counterpoint, and when all the parts come together a good choir can make the room absolutely ring.
A fugue is also correct for many cases - there are usually, if memory serves me correctly, echoed parts in all of the individual 'roles' in a fugue, but my memory is a bit fuzzy around the technicalities of it. I probably had a hangover that day (Thursday nights at the Sugarhouse, stumbling back at 4am were followed by an 8am dance lesson across the other side of town and then a 2 hour singing lesson, the bar stewards.)