According to the beamer-user-guide sections
16.1 (Inner Themes) and
16.2 (Outer Themes), the inner theme should "install templates for elements that are typically “inside the main text,” while the outer theme should "install templates for elements“ around the main text.
The way it appears to me now is that
beamerinnerthemetuhh.sty fulfill the same purpose in the flavor of an
outer theme as in the beamer user guide.
\andfunctionality for commands other than