Cutting from the stem of Joseph's Coat is Joseph's Coat. Cutting from a sucker could be JC or could be rootstock, depends on the origin of the sucker. If the rose was originally grafted, and the sucker is coming from below the graft union, then the sucker is rootstock. If the sucker is coming from above the graft union, then the sucker is JC (we usually call those "basal breaks").

See the photo at the link below to get a sense of where these can emerge (in the photo, they call the graft union "Bud Union").

Here is a link that might be useful: Anatomy of a bareroot rose