1) An Eastern Church member 2) Catholic church 3) Eastern christian 4) Eastern rite Catholic 5) Greek Catholic 6) Ukrainian Catholic 1) Uniat 
• (n.) A member of the Greek Church, who nevertheless acknowledges the supremacy of the Pope of Rome; one of the United Greeks. Also used adjectively.
adjective of or relating to former Eastern Christian or Orthodox churches that have been received under the jurisdiction of the Church of Rome but retain their own rituals and practices and canon law
a member of an Eastern church that is in union with the Roman Catholic Church, acknowledges the Roman pope as supreme in matters of faith, but maintains its own liturgy, discipline, and rite.
A branch of the Roman Catholic Church that preserves the Eastern Rite (Orthodox) liturgy and discipline but recognizes papal authority.