  We explore the nature of the long-wavelength mid-infrared (MIR) emission of a
sample of 13000 local Type II (narrow-line) Active Galactic Nuclei (AGNs) from
the Sloan Digital Sky Survey (SDSS) using 12 and 22 micron photometry from the
WISE all-sky survey. In combination with FIRST 1.4 GHz measurements, we show
that AGNs divide into two relatively distinct populations or "branches" in the
plane of MIR and radio luminosity. Seyfert galaxies lie almost exclusively on a
MIR-bright branch (Branch A), while low-ionization nuclear emission line
galaxies (LINERs) are split evenly into Branch A and the MIR-faint Branch B. We
devise various tests to constrain the processes that define the branches,
including a comparison to the properties of pure star-forming (SF) inactive
galaxies on the MIR-Radio plane. We demonstrate that the total MIR emission of
objects on Branch A, including most Seyfert galaxies, is governed primarily by
host star-formation, with about 15% of the 22 micron luminosity coming from
AGN-heated dust. This implies that on-going dusty star-formation is a general
property of Seyfert host galaxies. We show that the 12 micron broad-band
luminosity of AGNs on Branch A is suppressed with respect to star-forming
galaxies, possibly due to the destruction of PAHs or deeper 10 microns Si
absorption in AGNs. We uncover a correlation between the MIR luminosity and [O
III] luminosity in AGNs. This suggests a relationship between the SFR and
nuclear luminosity in the AGN population, but we caution on the importance of
selection effects inherent to such AGN-dominated emission-line galaxies in
driving such a correlation. We highlight the MIR-radio plane as a useful tool
in comparative studies of SF and nuclear activity in AGN.
