Yep, hotspot and corona! Lights with extremely deep reflectors (say Maglite 2AA LED or Ultrafire T6) produce coronas that are huge compared to the hotspot, almost half as wide as the spill. This is consistent with results obtained via ray-tracing simulations here.
Certainly! The latter (extending a shallow parabola) also makes it wider in absolute terms, which gives it a significant boost in throw.