Why are the white and orange wires both connected to my thermostat's W terminal?
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.