
I never said that it's a necklace to others and a collar to them. But as you can see in the manga the dom talks about giving him something to show that the sub is his and he gives him the necklace. After that the doctor also sees the necklace he is wearing and sees the meaning behind that necklace (aka showing that he has a master) and in return shows him his collar that he is wearing underneath his turtleneck. When the sub then returns home the master takes off the necklace (which serves more like a replacement for the real collar outside of their home because the sub probably wouldn't want to walk around with a real collar on broad daylight) and the master then puts on the real collar. There is no illusions HONEY. These are just different items to signal to the sub that he has a master and maybe even to other dogs if they were to approach him outside (in case of the necklace since I think that the dom engraved his name and his address or something on it)
He put a necklace on him and it turned into a colar
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