THE SHORT ANSWER
Take the pope out of Catholicism and you still don't get Orthodoxy; ask any Byzantine Catholic.
What you'll notice
You'll hear it from Catholics, Protestants, and the Orthodox themselves. Walk in from a Catholic Mass and the bones are familiar: bishops, sacraments, Mary and the saints. So the natural guess is that the Orthodox are Catholics who declined to sign one page.
What it's called
The pope's authority over the whole Church, which the Catholic Catechism calls "the perpetual and visible source and foundation of the unity" of the Church,1 is the largest single difference. It's far from the only one.
What's actually happening
Consider the Eastern Catholic Churches: they pray the Liturgy described in this guide and are in full communion with the pope (Who Are the Orthodox?). If the only difference were the pope, the liturgy alone would tell you which church you were in, and it doesn't.
The real differences include the filioque in the Creed,2 purgatory and indulgences,3 the Immaculate Conception,4 and above all how authority works. Orthodox bishops decide the great questions together, in council, and the Orthodox leave many questions deliberately undefined.5 Orthodox and Catholic has the full comparison.
Why it matters
Take the pope away from Catholicism and you get a church without its center of unity, which no Catholic wants. Orthodoxy is a different way of being the Church, where councils and the shared mind of the bishops carry authority, theology is prayed more than defined, and a great many questions are left open on purpose. Neither is a reduced copy of the other, and both would say so.
Where it came from
From the family resemblance, which is real, and from us: the shorthand is quicker than a history lesson at coffee hour.
What you do
If you're Orthodox: stop using the shorthand. It's unfair to both churches.
If you're visiting: if you're Catholic, notice what's different as well as what's familiar.
Go deeper
- Orthodox and Catholic.
- Timothy Ware, The Orthodox Church.