In the picture you provide, the white wire is going to an port labeled Aux. I would suspect that is for aux heat which may show up on the old system controller as emergency heat or auxiliary heat. Dual fuel usually is a heat pump (compressor outside) and electrical or resistive heat as the second source. By manner of elimination you can narrow down things. if it is heating and air conditioner and you do not see an exhaust stack connected to your inside air handler, it is electric for both heat sources, If it is propane or natural gas there would be a connection to chimney or forced air exhaust pipe and usually no backup with gas type heat, single source. If you have gas and see a coil with insulated lines going into furnace, that is for air conditioning and is single source cooling and single source heat.
