Also, this distinction can be clearly proved by the Holy Scriptures, although it doesn't need to be. But it is helpful if you're coming from a "Sola Scriptura" background, or in this case to debunk a false notion of "priesthood" as perpetuated by most Protestants contra Roman Catholicism.
The one example I can think of this offhand is:
The Catholic Epistle of St. James the Brother of God 5:14 -
Is any sick among you? Let him call for the elders (read: presbyters/priests) of the church; and let them pray over him, anointing him with oil in the name of the Lord.
Why couldn't any of the laypersons have done this? Why did it have to be the presbyters? Simple enough - it is because Holy Unction is a Sacrament/Mystery of the Church and sacerdotal grace can only be conferred by a validly ordained leader in the Catholic Church of Christ, who is either a successor to an apostle (bishop/episkopos), or an administrative extension of the presence of the bishop, which is the parish presbyter/priest.
Now God is certainly free to work the Mystery of healing through others, but this would not be the same as the sacramental Holy Unction which is given to an Orthodox Christian who approaches their priest in need of healing. I hope this additional point is helpful.