For any electrical circuit to work, it needs what is called a complete circuit...think of a circle. WHatever power goes out one side, must come back to the other. A short circuit is where the power doesn't go the intended path and takes a shortcut, which can often overload the supply that is protected by either a fuse or circuit breaker. AN example might be where the hot lead, instead of going through the load, got accidentally connected to ground or neutral - maybe by hammering in a nail to hang a picture and puncturing the cable hidden in the wall.
We don't really have 120vac coming into the house in the USA...we have 240vac from one side of a transformer to the other. WHen power is going out one side of the transformer, it's going into the other end. At about the middle of that transformer is what is referred to as neutral...so, it's 120vac from one side to the middle, and 120vac from the other back to the middle or 240 from one end to the other. When measuring things, it helps to have a reference. On our power, we use the neutral as the reference, and to give it a further reference, we attach that to ground. If you were to measure a 240vac circuit on one side to neutral, you'd get 120vac and the same on the other, but across the two leads (not using neutral), you'd get 240vac. A 240vac circuit does not use neutral. A safety ground is still often used. Many of the household things that run on 240vac also need 120vac, for example, an electric stove. IT uses 240vac for the heating elements, but often, will use 120vac for things like the oven light to make it easier since not everwhere carries 240vac light bulbs. Ground is for safety. There should not be any current on the ground, but it gives an alternate path for current if there's a fault to blow the fuse or trip the circuit breaker.
In an alternating circuit (ac), across a transformer, when power is coming out of one end, it is going back into the other. From one end to the middle, it would be doing the same, but in different directions. That's why in a shared neutral circuit, the actual current in the neutral might add up to zero, but the current would be functionally flowing from one end of the transformer back to the other end with the neutral point being balanced out to nothing (thus the neutral).
You're reading things correctly...there should only be the neutral connected to the ground at the main panel and separate wires run from there to any subpanel. This is to prevent there being ground loops.
Anyway, that's the thumbnail explanation, and there's all sorts of info on the web if you want further investigation.