I'm gonna put my in here. These are my thoughts and not the industry norm. So take it with a grain of salt.

The indoor coil technically is a hx. The definition of exchange is to give and receive. The air over the
indoor coil in cooling is giving. The refrigerant in the coil is receiving the heat. The refrigerant in turn is giving back a cold coil and exchanging the warm air for cold air.

In hp mode the cool air over the warm coil is giving to the the refrigerant inside, and the refrigerant is receiving the cool air, the refrigerant in turn is exchanging the cool air for warm air.

The term heat exchanger in a 80% furnace is not a true heat exchanger. Because the hx is not receiving anything from the cool air over it. It is only giving heat to the air and warming it. The flue gasses are not absorbing the cool air cause its not condensing or changing the state of the heat or flue gasses in the HX.

Now on a hi eff. furnace the secondary coil which is actually first in the air stream is a true hx cause the warm coil is giving heat. The flue gasses are receiving the cool air and are condensing. So there is an exchange of heat before the warm air passes over the primary heat exchanger.
Again these are not terms normally used in our industry interchangeably. Just trying to help you understand how things work.
Let the flaming begin.