Metal box and metal armored cable = Safety ground.
The “Line” is considered the wire the power comes from. It is typically 120VAC when measured to the neutral wire and 120 VAC when measured to the safety Ground.
The “Neutral” is wire the power goes out to. It is typically 0 volts relative to the safety ground.
The line and neutral are the wires needed to light a bulb or power a fan etc.
The “Safety Ground”, sometimes called “Equipment Ground” is a feature to protect the user and their family from deadly shocks.
When wiring a smart dimmer situations arise where the location you wish to install the device does not have a neutral wire. There is a strong temptation to use the safety ground in place of the missing neutral. This is not recommended (actually prohibited by law) and can bring unforeseen consequences if something else fails.
When considering using the safety ground in lieu of a neutral I believe people may only be considering the “normal” or 100% working case. The issue here is the danger that can arise when something else goes wrong or is wrong.
I’m not an electrician by trade, but when I was younger I worked summers for an electrician. In doing so I learned the basics. Since then I’ve only performed work on my house or for friends and relatives. Nothing major, only swapping out switches, receptacles, installing GFI’s etc. With this small exposure to house wiring I’ve seen:
Line and neutral reversed.
Receptacles strung in series where one wire is intermittent causing seemingly weird results when a light is turned or off.
Generally not so good connections.
I’ve personally had a good quality electric fry pan short out internally and was saved from potential risk by a GFI
Also consider the equipment ground was first introduced in the 40’s. It was recognized back then that a non-current carrying ground was required to keep users safe. So don’t think you know more than all those folks that preceded us just because you cannot readily see “…but why not…”
Finally, in the works of Buford T. Justice (aka Jackie Gleason) “… you can think about it, but dooon’t do it…”
The common conductor is the one that attaches to the black screw in a dumb switch setup.
In a 3-way line/load in separate boxes, the common is the constant hot in the line box and the switched hot to the load in the load box.
In a 3-way line/load in the same box, the common is the switched hot to the load in the line box and the constant hot from the line box in the other box.
Yep, it’s really a matter of context. If you ask in the abstract, the answer would be the neutral conductor.
But if you ask related to multi-way wiring, most electricians would say it’s the conductor that goes to the black screw. In fact, one unofficial technique when roughing in wiring is to wrap the “common” i.e. the black conductor that goes to the black screw a few turns around the other two conductors going to the switch so that it’s easier to identify when the box is provisioned.
In electrician speak, the common is as @Bry described. It connects to the black common screw on the switch. There are 2 common wires in a 3-wire circuit, the line power and the load. So, you need to know the wiring to know which one the common is.
Perhaps it would help to define the difference between common and neutral. It is my understanding that in the “ideal” case the line should come “in” on a black screw and the load should be powered from the other black screw.
UPDATED
And the neutral would be what I would call the common but perhaps this terminology is incorrect.
I said that wrong or at least misleading.
Was referring to the original question
In what context are you asking? Do you have a diagram from some datasheet that uses the word common.
To my knowledge a 3-way configuration has:
Line
Load
2 travelers
neutral
I only used the word COMMON in the above graphic to try and match the diagram to your question. In an actual installation it would be either line or neutral (preferably neutral)
I worked with electricians for about 5 years in high school and college and they never called the neutral a common. Maybe in other parts of North America they do.
Sometimes tied to signal ground depending on circuit. Telecom is -48 VDC based so positive of actually negative.
To answer @jeef let us know which type of path you have. Line/load same box or line/load separate box. If the first, then it would be load. If the second type then it could be line depending on where you put the switch.