One of the difficulties is that the Orthodox tend to explain their theology in Greek, and the Roman Church in Latin. Since the Schism, the Orthodox have not really defined or developed theological explanations as they depend on a Council of the Universal Church, which means to them, All the bishops in the World, East and West, not just thoes who show up. In the West, all bishops, East and West are invited to an Ecumenical Council when they show up, be it a few or a large number and the Council is ratified by the Pope, it is considered a Council by Catholics.
Transubstantiation is a latin term used to describe what and how the bread and wine become the Body and Blood of Christ, it was defined to distinguish the Catholic teaching on the Eucharist at a time (Council of Trent) when various Protestant sects were just forming and teaching alternative and conflicting ideas about the Eucharist. In the East there was never an attack on the Real Presence, so they never really had to make a formal dogmatic declaration.
As for Purgatory, most Orthodox believe much of what we believe, they phrase it differently and don’t use the Latin term we use. Not 100% the same as us, but a similar concept.