The distinction seems to be between being and doing, with the former being static and the latter dynamic.
I didn't work hard at all. I've never had a class which seriously taxed me mentally and until college at least I could get As without even trying at all.
Even more directly, on my first time taking the SAT (with 0 prep) I scored better than anyone else in my class, including people who had studied like crazy and gone through extensive prep courses.
Thinking that I'm anything but incredibly lucky would be arrogant of me. That being said, I do dislike the "gifted" terminology, primarily due to its theological and duty connotations.
Now, you can argue about interpreting IQ all you like, but it's really a moot point because the metric captures some of the variation humans have in cognitive ability. It doesn't mean that there's a neat linear scale (a simplification like IQ metrics leads some to falsely conclude this), but there is variation nonetheless, and it's mostly due to your genes, not your upbringing.
Does that mean you were gifted? Not necessarily; advantages in some aspects of cognition likely come with a trade-off for others. Those we consider gifted likely just have a good match of abilities with the challenges they face.
However, I would caution against the other extreme; you did not simply pull yourself up by your bootstraps in some sort of meritocratic Riefenstahl-ian fantasy. You most certainly had some advantages and fortune.
Please tell me how my success is due to my hard work and not the luck to have been born to my smart-but-relatively-poor parents.
I know other people can spend their life working hard and not get to where I am, and people can work less hard than me and get a lot further. This isn't a game with very structured rules. Life is chaos, and you're doing yourself and society at large a disservice by ascribing your success solely to "hard work", because applying that dogma to people with an IQ of 90 isn't going to work out well on a large scale.
(N.B. Amount of hard work still dwarfed by blind luck.)
But I agree that it's misleading to call someone gifted. Intelligence is such a diverse thing. Some people can be gifted for one thing and totally deficient for some other things. I'm not even sure that a very high IQ is predictive of success in science for instance.
Starting advantage does not mean you are not working hard now. Just means that you should do good things with that advantage. Make it shine!