Breaking the plane different types of T
 

I understand that if a defender breaks the plane on a throw in after a warning it is a team technical. I also understand that if they contact the ball it is a player technical with no warning needed. My question is does anyone know the logic why one is a team technical and one is a player technical? Is it because in the first instance perhaps a different player was warned, for any dog, than the one that broke the plane the second time.

Yes, that's the logic.

Isn't a DOG warning still logged for breaking the plane when there is ball contact on a throw in (assuming there wasn't one already)?

Yes, it serves as a DOG warning. So any subsequent water on the floor after a timeout, huddle during a free throw, interfering with the ball after a made goal violation would then also be a technical foul.