Maybe I can bring a little clarification into this discussion.
Clouds are classified by two things:
- height of base over ground and visible texture from ground observation.
Short notations are meant to be a combination of the two.
A cloud with classification starting Cumulo- is a low base heap cloud with usually vertical development and is the C in Cb.
A cloud with classification Nimbo- means a cloud with rain or precipation, but has nothing to do with the b in Cb.
Cb is a Cumulus cloud with a bossed shape, so a cloud which would usually develop vertically, but by reason does not and instead bulges on top.