there is now only "verbatim" and it should make sense to have the short form "verb". "verbatim" is more general for a lot of verbatim environments and the problem having verbatim code as arguments. "verb" is a specific tag for inline verbatim material.
I generally prefer tags that are about a concept to tags for a specific implementation of the concept. The exception is when the concept is to large as to be useful; then specific subtags are in order (e.g. the graphics tag and the tikz-pgf and pstricks tags; or fonts and fontspec). Also I prefer tags about packages to tags about commands.
The reason for this is that tagging should primarily help in finding information. If there are too much questions per tag, sorting by tag doesn't help much. If there are only very few questions per tag, then there are too many possible tags to look up and information gets distributed across too many places.
Anecdotal evidence has show that users don't particular care about which verbatim implementation does the job and are often unaware that there exist several implementations. As verbatim is a relatively low frequency tag, I don't see a reason to split it into implementations.
However, to avoid confusion, it might be sensible to rename so that it is clear that it is about the concept of verbatim input (maybe to verbatim-text?). Then if the need ever arises, we can easily add a verb sub-tag. (Though I doubt that that need will arise anytime soon: there are currently 5 questions that would be tagged with verb.)