Cumulonimbus or nimbostratus?

Recently I posted a question to the group concerning a phenomenon I had
observed in the vicinity of a thunderstorm. In that post I called the subject
cloud a "cumulus," and in the description I noted that it had extensive
vertical development, that there was another towering cloud nearby from which
heavy rain was falling, and that clear air prevailed in other areas of the sky.
A few days after that posting I received an e-mail message from a reader of the
group (who was not one of the respondents to the particular thread, which was
titled, "What was this STRANGE cumulus phenomenon?") advising me that I was
wrong, and that the subject cloud was NOT a cumulus but a nimbostratus.

This got me to thinking, and sent me to several "Meteorology 101" sites around
the Web. After further research, I concluded that I should have called the
cloud a cumulonimbus, but I came away with nagging doubts that my
corespondent's suggestion that it was a nimbostratus was correct.

I believe that that my description of the weather (in my original post) is more
in keeping with air mass convective activity (the description of discrete
towering cumulus, and clear skies elsewhere), than it is with frontal activity,
which I believe is where nimbostratus is found -- am I correct on this point?

Also, when I described it as a cumulus cloud, was I totally incorrect? I seem
to remember having been taught that cumulonimbus IS a TYPE of cumulus cloud,
that is, that cumulonimbus is a member of the broader family of clouds know as
cumulus. In any event, based on the description given, what should I have
properly called the cloud? Somehow, nimbostratus just doesn't seem to fit the
bill, but perhaps cumulonimbus is all wrong, too?

I thank the learned members of the group in advance for their answers.