Which of these verbs and nouns are the same or different, and what do they mean?
They're different because people speak casually.
What are the rules for when you can or cannot do (or use) them, for example, based on wire size?
Identifying wire categories
The three groups of colors are:
- Ground: Green, yellow w/green stripe, or bare
- Neutral: White or gray
- Hot: anything else.
Code doesn't make any finer distinctions unless you are doing stuff with a type of 240V 3-phase called "wild-leg". In particular, Code isn't that concerned with distinguishing hot wires from each other.
With #6 or smaller wire, the wires which must serve those purposes must be natively those colors.
With #4 and larger wire, you are allowed to use (within certain limits) wire whose jacket is the wrong color, and re-identify the wire by wrapping the ends with phase tape to re-color them. This rule is intended to relive electrical supply houses of the burden of carrying 3 different colors of large sizes of wire, and just carry black - and should be used in that context.
Also, in a manufactured multi-conductor cable of #6 or smaller, if the cable has a neutral colored wire and you want to use it as another hot, you can re-identify that wire using phase tape. This works from neutral to hot only.
Phase tape is a slang term that applies when re-identifying or really, when phasing individual phase wires. Don't get too hung up on nomenclature.
Totally separate from hot/neutral/ground is identifying individual circuits. Here's what you can't have: an EMT conduit with 5 #12 blacks and 3 whites in it. There would be no way to identify which hot(s) are matched up to which neutral.
On the other hand, if this #12 wire had 1 black and 1 white with blue tape on it, 2 blacks and 1 white with red tape, and 2 blacks and 1 white with brown tape -- now we know which wires are with which circuit.
Another acceptable way to mark the circuits is for those to be three cables in the conduit.
When we put blue tape on the white THHN wire, we are not re-identifying it as a hot wire - that's not even allowed.