Smithgd,
You are in general right. You can't use your CPL for anything, however, without a valid Class/Type rating, which you will have to revalidate every 12 months (24 for SEP Class).
The CPL and ATPL can be regarded as licenses permitting you to transport people/goods for renumeration, they do NOT allow you to actually fly any particular Class or Type of aircraft.
Cheers,
redbar1