I wanted to get a programmable thermostat, but when I look at the wiring of the existing thermostat I’m not sure why the white and orange wires are both going to the W terminal. 
Other thermostat wiring, located downstairs
At the zone board there are 3 orange wires plugged into it and one that isn’t plugged into anything. There is an orange wire in the first terminal of the HP and Duct area under the sensors section. There is also an orange wire plugged into the O terminal under equipment. I made a black mark on this diagram to show where orange wires are connected.
Best Answer
Your Existing Thermostat may not have been the proper thermostat for your unit. However it was made to work - utilizing a wiring trick.
The below is a rough guide for AC thermostat wiring.
Orange wire and Blue wire are usually a reversing valve.
RED, RED[c], RED[h] is 24VAC where c stands for cool and h stands for Heat.
W or W1 White (Heat Stage 1) , W2 [color can vary] (Heat Stage 2)
Y or Y1 Yellow (Cool Stage 1), Y2 [color can vary] (Cool Stage 2)
G Green - Indoor Fan (Evaporator Fan - Blower inside house)
E - Emergency Heat
EDIT 12/05/2017
I am guessing that the outside units are different model units - but it does not matter.
I am thinking that the orange wire might be the loose one on the other side. To know for sure - we already know that the orange and white are tied together on the thermostat side - so it forms a continuous run of wire (continuity) - measuring on the other end of those wires for continuity - we should see it as ONE wire and not two. So on our zone board side we take a continuity tester or better an Ohm Meter; you can get a cheap one for about $5-$10 . With your Circuit breaker off perform the following.
At your Zone Controller where the white wire from your thermostat unit should come in as W1 (disconnect it ) and Measure ohms between that white wire and each of the orange wires - one of them should show continuity if that Orange wire is any of those that feed to the zone board. This is how you can determine which Orange Wire is the wire form that thermostat - your meter should read less than about 3 ohms. You can then LABEL that Orange wire as Your Thermostat #1 or #2 which ever one it is and then report your findings back here.