This is a question that is often confusing to Catholics who have grown up in the Roman Catholic Church. You may wish to share with them this response:

After the Eastern Schism in 1054, eastern churches no longer in union with Rome came to be known as Eastern Orthodox or simply “Orthodox Churches.” Eastern Churches that remained in union with Rome are called Eastern Catholic Churches, or often the “Eastern Church.” An easy way to remember is this: “If the name of the Eastern Church as “Orthodox” in its title, it is not in union with Rome.

Eastern Churches accept the pope as the leader of the Church. Eastern Churches are fully Catholic. While all the Eastern Churches accept the authority of the pope, they also have a great deal of autonomy in Church life. They are governed by a separate code, called the Code of Canons of the Eastern Churches. This code helps to preserve some traditions that differ from the Roman Catholic Church, including the ordination of married men to the priesthood. Eastern Churches worship with their own style liturgy.  The Armenian, Byzantine, Coptic, Ethiopian, East Syrian (or Chaldean), West Syrian, and Maronite liturgical rites and certain other liturgical rites of local churches and religious orders have been recognized as authentic liturgical expressions within the Catholic Church. The three largest Eastern Churches are the Byzantine Ukranian Greek Catholic Church, the Syro-Malabar Catholic Church, and the Maronite Catholic Church.

Finally, what are “10 Frustrations Every Eastern Rite Catholic Understands”? This informative and fun article helps to answer that question!