Types of collars are as varied as the types of rings, some merely worn for decoration.
The contention when discussing this is that we use the same word for the act of declaring a closer bond and the item we use to signify it.
We don't do that with rings. One gets engaged and eventually married, we don't say they get "ringed".
So seeing a collar does not automatically mean you know the nature of the wearers' relationship.
Now, if you asked the question "what does it mean to you to be collared" you'll get a different flavor of answers. Still, some will answer with an adjective. Do you mean a play collar or a training collar or a collar of respect or one of ownership... so forget what I said, it is still an unknown.
We need better words. Like dating, going steady, engaged, and married. The verbs help us understand what the accompanying ring means.