You're right Sig, it's not a split system but an AC with a heat pump as well, it can reach into the 30's in January.
This is the issue with HVAC terminology sometimes.
What you stated makes no sense to me.
Generally with split unitary product, you have 1 - heat pump (outdoor HP unit with indoor air handler/blower which has the coil) 2 - Gas/AC or (indoor coil/gas furnace with AC outdoor unit) 3 - Dual fuel, heat pump (outdoor unit) with gas furnace and coil (indoor unit) .
If what you have is not a split system, it's a package unit.
Package units come in
1 - Gas pack (A/C with gas heat).
2 - Heat Pump (with strip heat for back up heat).
3 - Straight AC (very odd, generally I come across them in Florida, added it's getting to the point with overall sales, it's cheaper to buy a package heat pump or gas pack than a straight AC package unit).
4 - Dual fuel package unit. Combination of heat pump with gas for heat (back up heat generally) with no heat strips.
When looking for a "coil", you either have the indoor coil (coil inside a air handler or dedicated coil on a furnace) or outdoor coil (which is the coil on the outdoor condensing unit, or with package units, you have the condensing unit coil with evaporator coil.
What's happening with SEER rating is one of the coils (or both of them) are getting larger and larger (physically) for efficiency ratings.