Are 120V Feed Hot Wires in a panel/sub-panel Interchangeable

Up until 2011 the National Electrical Code allowed a "3 wire" method of connecting a sub-panel. This means you have the two "hot" wires and a neutral running to the sub-panel as opposed to the "4 wire" method where you add a separate equipment ground wire.

So, when your house was built, it was perfectly legal to use the 3 wire method. There is no problem with this unless you connect a metal pathway, such as a water pipe, from one building to the other. This allows neutral current to flow on this parallel path. This could be potentially lethal to someone working on the pipe.

As to the main panel not having a neutral: it does. If you look again you will see the two hot wires and a bare conductor. There is no ground wire on the service drop. The bare conductor is the neutral. This is allowed on the service drop, but from that point on all neutral conductors must be insulated. Ground wires are always allowed to be bare.

So, in short, there is no problem with your system unless you run a metallic system to the sub-panel building. This would create a problem.

The three wire allowance is an exception to 250.32(B)(1), which allows existing installations that were compliant with previous code versions to exist. If you want to bring the installation up to current standards, you can install a properly sized grounding conductor between the panels and separate the neutral and grounding bars in the second panel.

The reason you need to bond the neutral bar in the case of a three wire feeder, is to provide an effective ground-fault current path. Remember, electricity is trying to return to the source, not to the ground (earth). In the event of a ground-fault, you want the fault current to be able to have a low resistance path back to the source. This low resistance path should allow the fault current to be great enough, so that a circuit breaker (or other protective device) can activate and open the circuit.

If you read the text of the code, you'll find that it says "the grounded conductor run with the supply to the building or structure shall be permitted to serve as the ground-fault return path". By bonding the grounded (neutral) and grounding bars in the panel, you're using the grounded (neutral) conductor as a ground-fault return path.

Hope this makes sense, and answers all your questions.