Sorry all. You put too much meaning on the collar per se. It is the same as a ring.

It can mean everything, or it can be as simple as a piece of jewelry.

Collars can be used as an adornment, in play, as a token of friendship, as a token of intent (ala an engagement ring,) as a token of commitment, and as a token of ownership. As a token of ownership, you could be mere chattel, a pet, an "animal", a beloved prize, or a loved and cherished partner.

Being collared is no more nor no less than whatever it means to the two people involved in the exchange.