Is CM under the classical approach/method?

So on my HS forum, I blog and write articles.  I am doing a series on the styles of HS’ing, and in doing some research on the trivium (classical) approach, I found that it lines up remarkably well with the CM approach.  So this made me think that maybe there are methods, and then there are approaches to those methods.  On my forum, someone suggested that CM, Sonlight, Heart of Dakota, and My Father’s World are approaches to using the classical method.  What are your thoughts on this?  Would CM fall under the broader category of the classical approach?

Along these same lines, upon researching the Montessori method (used in some schools), it seems to fit “unschooling” very well.  Are there different names for approaches/methods based on where they are being used (traditional school vs. HS’ing)?