Donna
You certainly got some excellent info in the posts above, but must be feeling a bit overwhelmed trying to absorb it all.
Let me suggest a single website that provides a brief explanation of each of the Eastern Catholic Churches, Byzantine and otherwise. It is relatively up-to-date and accurate and contains most of the information that you would find in Father Roberson's book, which someone recommended above.
CNEWA: Eastern Catholic Churches [
cnewa.org]
The same site also provides info on each of the Orthodox Churches, which will be of interest to you also, to better understand the history and differences/similarities between the two lungs of Eastern Christianity.
If you are looking for more detail on any of the Churches
sui iuris, you might want to read another recent thread on this forum. A list of informative websites relevant to each Church
sui iuris are posted there (altho the topic is titled "Byzantine", there are references there to all the Churches
sui iuris).
FAQ for Byzantine Catholics God grant you many years,
Neil