A 16 SEER heat pump usually has one two-stage compressor. The first stage is usually 75% (approximately) of the rated tons. The second stage runs at the full compressor rating.

Not sure about the 18 SEER Amana. The Trane XL19i has 2 separate compressors. The first compressor runs at 50% of the rated tonnage and the second compressor runs at the full rated tonnage. In this set-up, one or the other compressor is running (not both).

Just because the heat pumps are rated at 16 or 18 SEER does not mean that the system is rated at that SEER. The matching air handler/furnace is critical in maintaining that SEER rating. An air handler/furnace can decrease SEER, increase SEER, or support the SEER rating. This is why it is important to know thw model numbers of both the condenser (outside unit) and air handler and a/c coil if there is a furnace involved.

A heat pump with either a two-stage compressor or dual compressors has 2 stage cooling. If the same heat pump has auxillary heat in the air handler (back-up electric strips, gas furnace, etc), it has 3 stage heating.

FYI, you don't necessarily reduce your utility bill with a 19 SEER as compared to a 14 SEER. The Energy Efficiency Ratio (EER) determines your true operating costs, not SEER.

The 18 SEER Amana is a two-stage compressor just like the 16 SEER. SEER ratings are between 17 and 19 depending on system size and matched air handler selected.

If you go Amana, make sure that you get the optional thermo-static expansion valve (TXV) installed in the air handler. A TXV regulates refrigerant flow to the evap coil much better than the flowrater piston that is supplied with the air handler. All SEER ratings for Amana systems are performed with a TXV.