Earths, Grounds, Neutrals, Hot leads, and Safety grounds.
Earth Ground: (I use the double term to be clear for readers on both continents) It is just what it sounds like, a connection to the earth. (Preferably fairly well connected and in the same neighborhood as my bare feet.)
Neutral: The side of a power circuit that is connected to earth Ground. This connection (called bonding) is only allowed to be made at one point, and that is in the service entrance box. (Actually it is connected at two points in many systems, but one of them, out at the power transformer, is not under our control.) But let us not confuse that restriction with connecting OTHER things to earth ground.
Hot Leads: The side of a power circuit that is NOT connected to earth ground in normal operation. Note: this is not an official description found in the electrical code books, but you all know what I mean.
Grounding Conductor, Safety Grounds: (Equipment Grounding Conductors) Connections from the exposed non-current carrying conductive parts of all electrical equipment to Earth Ground. (The bare, green, or green with yellow stripe wire.) These safety grounds are NEVER supposed to carry any part of the normal load current. This is the reason why they are to be connected at ONE and only ONE point to the neutral wire. If they were to be connected to the neutral conductor in more than one spot, then any load current flowing in the neutral conductor would divide between the two paths.
Because the connection (bonding) between the earth ground and neutral leads is already made at the service entrance and/or at the outside power transformer, we are not ever allowed to make that connection again inside of any of our equipment. Thus we have 3 wire cords, even when 2 of them have nominally the same voltage on them. The reason that the safety ground is there is for when (note: not if, when) something goes bad inside of a piece of equipment, and the power lead gets connected to the conductive parts of the case. As soon as this happens we want 2 things to occur.
Let us think about the typical HO layout. It contains lots of exposed conductors. Are any of them connected directly to the mains power? I sure hope NOT! Not either to the Hot nor the Neutral sides. Are the DCC boosters connected to mains power? Again, no, they are fed via low voltage transformers. However, what if a transformer was to fail? In that case it could be connected to the hot side of the power, so I for one would recommend that the cases of all boosters be grounded for safety reasons. (Because I prefer copper grounds to barefoot grounds.) In addition, if you are providing your own power transformer for a booster, (rather than purchasing a commercial listed unit) you should connect the transformer case itself to the safety ground. (my interpretation of the intent of NEC section 250-45) Remember, we can connect as many things as we want to earth ground via safety leads, and at as many places as we please. (Except that neutral wire which is limited to one place in a building.)
My personal rule is simply to ground anything that could possibly accidentally get connected to both a power lead and to me at the same time. I also have installed GFI circuit protection for all of the outlets in my layout area, and a master power switch for them. No, I do not wear both a belt and suspenders! I just want to be sure that that soldering iron or hot glue gun gets turned off when I leave, even if I forget to unplug it. Let me also make a comment on GFI breakers. They are used to detect a flow of any current from the hot lead that is NOT returning via the neutral lead of the same circuit. The assumption is that it might be returning via my bare feet, and that it would be useful to immediately stop this faulty ground (which is probably not good enough to trip the breaker) by opening the circuit. (Well worth the cost, since I have not yet mastered the trick of keeping both feet in the air at the same time.) If you do not have GFI protection on all the outlets in your railroad area, please immediately go and spend the $10-20 needed to do it. (Only one GFI outlet is required to protect all the other outlets located down line from it in each circuit.)