TB, I think that the wedding introduction of Tom to Kay was for the audience's benefit. Not everyone in the audience had read the novel, so the film script let's those audience members know Tom's relationship to Michael. The same is true when Michael introduces Fredo to Kay. You might note that when Michael introduces Tom to Kay he afterward adds that Tom is probably going to be named Consigliere. He does so without enthusiasm. But that part of the scene is telling because Michael adds that Tom is not a Sicilian. While that is true, it's unnecessary for Kay to know.

As we've opined in other threads, when Michael speaks with Tom after the attempted murder of him, Michael is simply manipulating Tom with his brother comment. Realistically, Michael doesn't (and can't) trust anyone else. However, he knows that Tom is loyal to Vito (and thus the Corleones) to the end. So, Michael's referring to Tom as brother in that conversation is simply Michael's manipulation of Tom's loyalty when Michael has noone else to turn to.