Plasmonic nanocavities with sub-5nm gaps between nanoparticles support multiple resonances possessing ultra-high field confinement and enhancements. Here we systematically compare the two fundamentally different resonant gap modes: transverse waveguide () and antenna modes () which, despite both tightly confining light within the gap, have completely different near-field and far-field radiation patterns. By varying the gap size, both experimentally and theoretically, we show how changing the nanoparticle shape from sphere to cube alters coupling of and modes resulting in strongly hybridized () modes. Through rigorous group representation analysis we identify their composition and coupling. This systematic analysis shows modes with optical field perpendicular to the gap are best to probe the optical properties of cavity-bound emitters, such as single molecules. Effective ways to enhance, confine, couple, and utilize light down to the single-emitter level have been central questions of nanophotonics 1-3. Plasmonic nanocavities made of noble metallic nanostructures have played an important role in addressing this, using collective charge oscillations of surface plasmon polaritons 4,5. Surface plasmons on closely-spaced multiple nanostructures can hybridize with each other to create trapped modes within their gap 6. Such nano-gaps are used to probe optical properties of single-molecules such as their Raman scattering 7-9 , non-linear effects 10 , chiral activity 11 , or rate of emission 12. However, resonant enhancements depend strongly on the morphology of the gap, especially when gaps