Right, I suppose I did leave it very vague.  Well to put how I had imagined it into words, after the magic takes hold everyone besides the target and Eris spot viewing them as a 'person' per se.

In the case of a pet, that person has always been a pet to the owner, regardless of age difference.  Individuals then get to apply them own principles on the treatment of said pet, like lobbying for rights and how they should be treated, but otherwise will refer to them as a 'pet' if asked what they are.

For the transformation card, the recipient believes they always had the abilities they gained and is free to do as they wish with them. They are also aware that the target is trapped in them and vaguely keeps the same disposition towards them.  The target is only vaguely remembered by others as a missing person and quickly dismissed if mentioned.

I hope that clears some of it up for you.  I know mentally how I am going to be handling those cards so I didn't bother going into detail with how they work and as such I apologize for any confusion.