What is the difference between Eastern Orthodoxy and Eastern-rite Catholicism?
I have two questions for you about Eastern Orthodoxy and Eastern-rite Catholicism. First, what is the main difference between them (other than that one isn't Catholic and the other is)? Second, where can I go for a basic, general history of Eastern-rite Catholicism?
The main difference between Eastern Orthodoxy and Eastern-rite Catholicism is ecclesiological--it has to do with what each perceives the nature and structure of the Church to be.
The Orthodox view the Church as a federation of local churches, while Catholics, Eastern-rite or otherwise, see it as an organic communion, with the successor of Peter--the pope--as an essential component of that communion.
Despite this and other differences we can't consider here, there's a great deal Eastern-rite Catholics and Orthodox have in common, including a mutual cultural and liturgical tradition.
As a result, many Eastern-rite Catholics prefer to think of themselves as "Orthodox in communion with Rome" rather than as "Uniates," the latter term being one used frequently in a derogatory sense against Eastern-rite Catholics by the Orthodox.
In answer to your second question, for a good overview of Eastern-rite Catholicism see Hubert Jedin's History of the Church, vol. IX, pp. 335 ff. and vol. X, pp. 473 ff. The New Catholic Encyclopedia also has articles on the subject and many related topics.