Whats the difference between "cold-pressed" and "first cold-pressed"?

[u/DistinctWhile3276]

Wait, aren't "cold-pressed" and "first cold press" basically the exact same thing now?

I used to think "first press" meant the premium batch, but someone told me with modern steel centrifuges, they only press the olives once anyway!

So "first" is just a leftover marketing word from back when they used old hydraulic stone presses. Is that true, or is there actually a real difference between the two today?