As for your second question first let's clear up that DC Common, (i.e. negative, -), is not the same thing as Earth Ground. DC Common is the common return path for DC circuits. For example, your PC has a power supply that outputs +5V, +12V both of these voltage share the same DC Common (which is typically referred to as 'ground'). If you take a volt meter and measure from DC Common to the 5V output you get 5V, and from DC Common to the 12V output you would see 12V. It is the common current return path for each circuit.

Earth Ground is actually a connection to the Earth outside your home/shop. It's purpose is to increase safety and secondary provide a low impedance path to bleed of noise. It is NOT a current carrying path for your circuits. It is common practice to (earth)ground each sub assembly back to a common point and then to bond that point to your electrical systems (earth)ground. For example a DC power supply typically has an (earth)ground terminal that connects to its case. This (earth)ground connection helps to bleeds off electrical noise that might otherwise be radiated by the power supply but more importantly if insures that the case of the power supply will never go above ground potential and be a shock hazard. You do not want to go around connecting DC Commons to (earth)grounds unless you have a very compelling reason.

A ground loop is created when a voltage difference is created between two devices due to current flowing through a ground connection. For instance if you daisy chain an (earth)ground instead of star grounding it. Many power supplies will have the DC Common bonded to (earth)ground inside of them, if you create separate (earth)ground externally you could potentially create a ground loop by providing a path for DC current to flow through the (earth)ground.

Jeff i am trying to get to grips with this.

Is it ok then that all/any of the fixing holes of any circuit board can go to earth ground

Specifically the Smooth Stepper has a jumper for connecting 0v dc to that mounting hole is that OK to then connect that to earth ground

Thanks
Phil