The Orthodox Church, in my opinion, makes it very clear that they believe it is the One, Holy, Orthodox, Catholic, Apostolic Church established at Pentecost and continues today. Yet, it recently has broadened its willingness to talk with other sects.
In keeping with the church's teaching on universality and with the Nicene Creed, Orthodox authorities such as Saint Raphael of Brooklyn have insisted that the full name of the church has always included the term "Catholic", as in "Holy Orthodox Catholic Apostolic Church". The official name of the Eastern Orthodox Church is the "Orthodox Catholic Church".
They put ecumenicism this way.
Why have the Orthodox churches decided to be involved in the ecumenical movement for the unity of God’s Church, and how does this involvement relate to their claim to be the embodiment of the One, Holy, Catholic and Apostolic Church?
There is the belief that God's Spirit still works in the sects.
The belief of St. Cyprian that outside of the canonical boundaries of the Church there is no salvation must be respected as a strong urge to maintain and respect the unity of God’s Church. However, today’s needs require it to be supplanted with the theology of schism advanced by St. Augustine. For St. Augustine, schismatic and heretical communities, in spite of their formal separation from the una sancta, continue to maintain bonds of unity with it. All the separated Christian churches are related to each other and in communion, however imperfectly, with the One, Holy, Catholic and Apostolic Church. The recognition of this relationality is warranted by the fact that there are many still unbroken bonds whereby the schismatic communities are held in certain unity with the One Church. These bonds, in the words of Florovsky, include " right belief, sincere devotion, the Word of God, and above all the grace of God, which ever heals the weak and supplies what is lacking." There is thus in every schismatic and heretical community something of God that connects them with the life of the God’s Church. "What is valid in the sects is that which is in them from the Church, that which remains with them as their portion of the sacred inner core of the Church, that through which they are with the Church. "
So, to answer the OP, it appears to me that the Orthodox view Catholics and Protestants as "separated brothers and sisters in Christ" who have fallen from the truth, but who nonetheless retained some validity and are thus part of the Church.