Why SEER became SEER2 and HSPF became HSPF2
DOE updated the test procedures used for residential central air conditioners and heat pumps, and the current rating names reflect the newer test framework. That means old SEER/HSPF values and newer SEER2/HSPF2 values should not be compared as if the number changed only because a label was renamed.
For shopping, use the rating system shown on current certified data and compare like with like. If you are evaluating an older installed system against a new one, expect some conversion nuance rather than a perfect one-number comparison.
COP makes the heat-pump idea easier to see
Electric resistance heat converts electrical energy into heat at roughly one unit of heat per unit of electrical energy at the point of use. A heat pump moves heat instead. A COP of 3 means the system is delivering roughly three units of heat for each unit of electrical energy entering the heat-pump process at that condition.
COP is not fixed. It changes with outdoor temperature, indoor conditions, compressor speed, defrost, and the equipment itself. That is why a single COP should not be treated as a full-season prediction.
Turn ratings into a cost question
Efficiency becomes financially useful only after you combine it with a load and an energy price. HVACBird's heating-cost tool lets you enter an annual delivered-heat requirement, electricity rate, gas rate, heat-pump COP assumption, and furnace AFUE. The result is transparent enough to change one assumption at a time and see what drives the answer.
For cooling, the SEER2 estimator uses the rating with a capacity and equivalent full-load hours to produce a planning estimate. Neither tool is a utility-bill guarantee; both are designed to make assumptions visible.