Hi,
I noticed your question on the message board at ancestry.com. I am Byzantine Catholic and have a strong church history in my family. Yes, Byzantines used to be called Greek Catholic. They are the same. Simply a change in name. You may find this page very helpful:
http://en.wikipedia.org/wiki/Eastern_Catholic_ChurchesThe Greek Catholic Church consists of the Eastern Catholic Churches which follow the Byzantine (Constantinopolitan) liturgical tradition and are thus in full communion with the Bishop of Rome, the Pope.