I’m not sure about the origin of the words “Militant” and “Triumphant”, but they are words used by the Church to describe to two sections of the Faithful that exist.
Church Militant refers to the temporal Church (the Church that exists in time, on earth). It is “militant” because we are fighting a constant spiritual battle, both for ourselves and for the world. We know the outcome–Christ won victory for us on Calvary–but we haven’t finished the War yet (kind of hard to think about logically, I know.)
Church Triumphant refers to the eternal Church in Heaven. The members of this Church (i.e., the Saints), have “won the race” as St. Paul would put it. They have lived their lives in service of God and have achieved Eternal Salvation. They are therefore “triumphant” against the powers of evil.