CMP and SR:Missions are functionally pretty close to identical, at least in the ways you're asking about. They're both part of the living campaign, characters can be used in both and transferred back and forth to both, and you can use pregen characters with both (although for obvious reasons it's recommended you create your own character). In those areas, there's no difference between SR:M and the CMP's.
To my knowledge, the only difference between them is the story. SR:M has a couple of story arcs it follows, CMP's have different story arcs. It also seems like SR:M has a bigger focus on the overall arcs than CMP's do.