There is a difference between what USCIS calls a Visa and what the rest of the world actually means when they say a Visa. For eg. Green Cards (== aka Permanent

There is a difference between what USCIS calls a Visa and what the rest of the world actually means when they say a Visa. For eg. Green Cards (== aka Permanent Residency, which no one in their sane minds calls a Visa), are actually issued against what USCIS calls a "visa number". So OP is correct that O-1 is a visa (as that word is understood generally in the world), and EB-1A is a category of Employment Based Permanent Residence filing.