Both the Roman Catholic and Orthodox (including Oriental Orthodox) believe in the "one, holy, catholic an apostolic church," as stated in the Nicene-Constantinopolitan Creed, but what we mean by that is somewhat different. For Roman Catholics, the full catholicity (or universality) of the Church of Christ is manifested only in the person of the Bishop of Rome, whom they regard as the "Vicar of Christ" and as the "Supreme Pontif." For Orthodox Catholics (and again, this includes the Oriental Orthodox churches), the catholicity of the Church of Christ is manifest in the local church centered around the local bishop. My bishop, for example (His Grace +Thomas of Oakland and the East) is equal in ecclesial authority to any other Orthodox bishop.
I actually prefer, rather than refer to myelf as Greek
Orthodox or Russian
Orthodox, since I am neither Greek nor Russian nor Arab, to refer to myself as an Orthodox Catholic. This title expresses fully what we believe about our Church: it is the Catholic Church of the Nicene Creed, which has kept the faith in its full Orthodoxy. In the West, however, and understandably so, many Orthodox are wary about being confused with Roman Catholics, so they don't call themselves Catholic. But we are. We are Catholics in the fullest and most orthodox sense of the word.