The combination of words and design is considered a single mark to be registered.
I think Jim is right, essentially, but the words and design may
be registered together, they don't have to be. That is, they're not necessarily considered a single mark, but may be.
Neither a composite registration (in the case of a logo plus words) nor a registration of stylized text offers as complete protection as a combination of registrations (i.e., registrations for each element plus a composite registration). Practically speaking, one receives significant protection with only a registration on a composite mark, but not the best possible protection.
My advice is generally as follows. Where finances permit, one should opt for the combination of registrations. Where finances don't permit multiple registrations, one should opt for the composite registration.
I'm happy to expand on this if anyone is interested.