The spelling is interchangeable. Kantor with a "k" is a German spelling, while cantor with a "c" is an English spelling.
Kantors such as Southern Lutheran Kantor, Chris at Lutheran Kantor and Cantor Magness at Fine Tuning, not to mention Kantor Henry Gerike at the St. Louis Sem act as overseers for the music life of the church.
You might find your kantor conducting the choir, worship planning with the pastor, playing the organ, teaching a new song before service, organizing instrumentalist for Easter Sunday, teaching music in a church's grade school, or composing music for a worship service.
There is another type of kantor/cantor, though, and this one is normally spelled with a "c". A church may have a cantor just to lead in the singing of the psalms, hymns with a verse and refrain, gospel acclamations, and other selections. Generally, you might find this type of cantor singing from the front of the church, either at the lectern or perhaps off to the side.
This kind of cantor most likely wears just one hat. This cantor's participation in a given psalm might look like this:
For the purposes of this blog, "kantor" with a "k" will refer to the person who oversees the music in a parish or educational institution, and "cantor" with a "c" will refer to the person who leads the congregation in singing.
Kantors and cantors have held parish positions going all the way back to ancient Israel. For a five minute preview of cantoral contributions at the beginning of the Jewish High Holy Days, click here.
One famous Kantor was Johann Sebastian Bach. During one of his tenures, he composed one cantata per week for the Sunday service.
Like I always say, "If it ain't baroque, fix it!"