A twin is 2 individuals.
They are not a package deal.
They/the parent, has to understand, that "both" twins cannot always just go somewhere or with someone, if one is friends with someone and the other is not.
It is not, a package deal.
My friend has twins... she said that each twin has their own friends. She did not, expect EVERYONE they played with, to invite BOTH girls each time. It is a burden, for other kids to think that and for that other parent too. And it is presumptuous... to think that both twins, has to be at all outings, even if one was invited and the other was not. ie: each twin is an individual and has their own friends. So she knows that and did not in any way, 'expect' invitations to ALWAYS be for BOTH twins. Each of her twins, has their own activities/interests/friends.
If I were you, I would just invite "Johnny" to a play-date. Just say to the Mom "My Son would like to invite Tommy to come over." Then as needed, just explain... that your son 'Johnny' is closer with Tommy than her other twin Jimmy. And bonds more with that one.
It is nothing personal.
It just is.