Thanks for the explanation with regards to the semantic differences between rite, church, and tradition.
I must respectfully disagree with the comment about "...the terms "uniatism" and "uniate" must never again be used."
The terms uniate and uniatism are, to a certain extent, being used as mild insults by our Orthodox bretheren. Words do have power. But I think in this instance it's only because we as eastern Catholics give it that power. Perhaps a better approach is to simply adopt those terms as our own.
Some of the the Orthodox seem to have some problems with the existence of the eastern Catholic churches. And let's face it, we need only go back about 50-100 years in history to see some serious problems with the treatment of the eastern Catholic churches at the hands of the latin Catholic church. But the point is, in spite of it all, we're still here and we're not going to disappear any time in the forseeable future.
"The terms uniate and uniatism are, to a certain extent, being used as mild insults by our Orthodox bretheren."
O fiddlesticks. If I want to insult the people of the Unia, I can do much better than to call them Uniates. The term is handy. The term is descriptive. If people of that persuasion find the term offensive, they really do need to get a grip.
The reality for the Uniates is simply this: They are a tiny minority within the Roman Catholic organization and they therefore get little respect from within it(as measured by clout). And they are viewed by the Orthodox as perfidious, pathetic, and pitiful at best. They have, however, contributed some important scholars. But so also have the Anglicans, for that matter.