The old mercury bulb, 4 wire thermostats were simple switches which connected red to green for fan, red to yellow for compressor, and red to white for heat. All the rest of the logic and power switching is done in the noisy parts of the equipment. These can be examined with an ohm meter.
Modern digital thermostats make the same connections but they are equipped (plagued) with time delays and resets that make checking all the triacs take nearly half an hour. You can not check them with an ohm meter. You have to apply 24 VAC and measure for an output voltage.
If you have a heat pump or a fuel burning furnace, the Blue and Orange connections come into play as logic signals to the change-over switches and valves. Which kind do you have?
Many digital thermostats use a Miniature relay, if you can get it to operate around the set point, listen for the relay click, check the output with an ohm meter, if it stay open, it is usually the relay contacts shot.
Max.
I have seen the honeywell relay thermostats as well, used in industrial water & hydraulic cooling units, but never seen them in residential applications.