I think it’s quite important to note the way Castle and Beckett take the mug from the other. In the first gif Beckett is silently telling Castle “Thank you”, her hand caresses his in a very subtle and soft way that is like a light morning kiss. In the second, on the contrary, Castle takes the coffee opposite to Kate’s hand; his hands barely touches hers, he is almost hesitant about touching her or taking the coffee at all. And it’s in this moment that Beckett understands how much he is full absorbed in his own pain that she almost doesn’t exist for him. How much he is worried for her daughter, that her being there or not would make little difference to him. And this transpires in the fact that he doesn’t even want to accept her coffee, at first, that he is almost afraid to touch her. She would want to help him, but she totally feels that in this case he is quite totally unreachable, leaving her completely alone.