The answer to:
returned: "To please all."
That might be more of a matlab in-joke, but a true answer can only (possibly) be given by Mathworks and this seems unlikely to happen - for reasons of business-privacy reasons, and even if they tried it would likely not be a complete and correct answer due to the "fog of time". The two functions are in different toolboxes, cconv is in my signal-processing toolbox, while conv is in the datafun toolbox, this makes the former an add-on while the latter is included in even the most basic matlab-package. To my memory the conv-function is older than cconv which makes its existens if for no other reason an issue of backward compatibility. In addition conv also allows the setting of the output size by the flags 'same', 'valid' and 'full' which my version of cconv does not.
This answers your question.
As an advice for programming for other users that might not have the same toolboxes available check what toolboxes you are using by checking which functions you are using. You can do that by explicitly calling which:
and get the full list of which cconv-functions you have, or after the completion of your function/script/toolbox you could use: