Gas heats hot water in tank. Hotwater goes to furnace and heats air. Cold water returns to hot water tank.
Separate AC (1995) unit outside.
In winter you need to flip a switch to "heat", and in summer you need to flip same switch to "cool" for the heat / AC to work respectively.
BUT, this time of year (AC) the upstairs of my house is quite hot, mainfloor cold. Even when i turn the thermostat on main-floor way high (say, 80), and upstairs cold (say, 69), the main floor is cold, upstairs is hot.
Pretty typical problem for a 2 story house. Likely has little ductwork to the second floor, as in the old days they only sized and placed ducting for heating (no AC) so the heat would naturally rise to the second floor (so little ducting needed there).
You can run the fan in the "on" position continuously and that should help to keep the air a more even temperature between floors. If there are some registers you can turn down on the main floor (without loosing too much the airflow through the furnace) that may also push more air upstairs.