So this is an interesting topic, at least to me. Anyway I'm going to define my terms up front. This is likely to be the last bout of theory for a good while as I'll start to work through my backlog of posting links.
Symbolic-collar or Collar (capital C): a general term for a token used to acknowledge a power exchange. Collar may also refer to the exchange relationship itself.
Physical-collar collar (lowercase C): An object that closes or wraps around the neck. A physical item worn by a person.
Collared: A person may be said to be "collared" when they wear, or experience, a Collar. Being part of a power exchange relationship, no matter how small scale, subtle or individual.