We are Roman Catholic - fully Roman Catholic. The Ordinariate ( to which individuals as well as parishes have to be admitted - there is an application process) allow parishes to function together kind of like a diocese, but obviously not bound by geography. The Eastern Rite Catholics ( I assume you are not including the schismatical churches) are in union with the pope but maintain their own rites, have their own patriarchs, etc. I've heard it explained that they are essentially the same as before the great schisms. What they are NOT is Latin - unlike the parishes of the Ordinariate. The churches of the Ordinariate are using the Anglican rite which is actually closer to the rites of the church at the time of Henry VIII than the current RC rites, or so I've been told. Well, other than the fact that it is in English, of course. That is my admittedly limited understanding of the differences.
eta - Found a good overview of Roman/Western vs. Eastern - not specifically the Anglican Ordinariate, though - our priest faces the altar, for example, and our architecture and art are far more traditional and ornate than that in this chart.
http://www.stmarysbc.com/faith.html