Thermostat Wiring Problem
Red-white setup is heat only. When closed it means a call for heat. My thermostats are Ritetemp 8030C, but I believe that wiring convention is same throughout.
Red is a sort of shared wire, and can also be used in conjunction with 'Common' (blue in my case) to bring 24VAC power to the thermostat so it does not use up batteries. Thermostats also often have separate RC and RH terminals(connected by a jumper wire), in case heating and cooling units are separate and there is a red wire coming in from each.
Heat is controlled by W (white) wire, which is closed to red when thermostat calls for heat.
Cooling is controlled by Y (yellow) wire, which closes to red when thermostat calls for cool.
And fan is controlled by the G (green) wire.
There are other, more complex setups with secondary heating/cooling units etc.
If your unit is heat/cool, it should at least have R, W and Y terminals, likely G as well. The problem it seems, is the wiring - is wiring older than the HVAC unit? If so, you need to upgrade it. I recommend 18/5 thermostat wire. I recently bought a 250' spool of Honeywell 18/5 on ebay for about $50.
Looks like you'll need a more advanced thermostat as well.