This is sort of a goofy-sounding tag. I'm not sure what the guy who thought this one up had in mind, but I think that "applications" or "applied-science" would be a better wording.
applied-theory, applications, applied-science make no sense. A tag notes a sub-domain, a topic, a class of questions that people will be particularly interested in or particularly not interested in. Distinguishing between theory and applications (as opposed to particular theoretic or applied domains) is useless.
Let's get rid of applied-theory.
I think I created it. The rationale was probably the wish to tag applied questions, that is not purely theoretic (as in TCS, but also as in purely academic) ones, so that people not interested in theory can easily grab what they want.
I still think it can be a useful tag. We have not used it consistently, though, and should start doing so if we decide to keep it.
The name can certainly be discussed. applications is bad, imho, as it is ambiguous for people that do not have a (formal) CS background and do not bother to read FAQ and tag excerpts; given the amount of mistagging we have, this seems to be real danger (even if maybe not a problem). applied-science sounds as if it included more than computer science, but this is not a problem in the context of this site. It also fits above motivation better.
Tl;dr: Keep the tag, but rename to applied-science.