Earlier quoted context omitted.
They're the same thing if your day-to-day productivity requires invention, as it does in Carmack's case (and I would argue most programmers)
They are not the same thing, unless they achieve what a 1x programmer won't on a lifetime on a day-to-day basis. If the 10x, 100x or 1000x programmer does not do the 10x, 100x or 1000x times on average on their day to day then they are not 10x, 100x or 1000x programmers. (for whatever the heck a 1x programmer is, which people talking about 10x programmers oddly always skip on giving any decent definition)
The best programmers can produce code every day that a mediocre programmer cannot ever produce under any conditions. That is the entire point of the discussion.
I don't even think it's that controversial of a statement, just shift to another field and I think it's self-evident. Paul Erdos could on any day produce better mathematics than the rest of us could produce in a lifetime. Not better maths than his peers, but his peers were also exceptional. Better than the average person who knows how to do their times tables though? Absolutely.