Of course, the Roman Catholic Church would claim to be orthodox, while the Orthodox Church describes itself as a Catholic and Apostolic church. But generally speaking, "Catholic" is used to refer to the Church led by the Pope, while "Orthodox" is used to refer to the Churches led by the various Patriarchs.
But I mean, at what point did these words begin to be used to generally identify the Western and Eastern Churches? At what point would you have someone arguing "Our Catholic Church is right and the Orthodox Church is wrong", and this being something people could understand? Was it immediately after the Great Schism, or much later? Or earlier?
Are you asking about the cause of the east west schism, or about the use of the words Catholic and orthodox to refer (at least to lay people) to the two religious organizations?
Catholic does not mean the church is run by the Pope. Oddly this is the second time today that I have seen this inaccuracy mentioned here. Catholic means that you hold that your church descends from Jesus through the apostles and the various councils eg that you are the correct church. When the Anglicans say the Nicene creed they claim "I believe in one holy Catholic and Apostolic church". They are not proclaiming the legitimacy of the Holy See they are claiming that they are the true faith.
The Orthodox churches are Catholic churches just not Roman Catholic Churches.