Tough call. I've trained martial arts for years and would be fine calling myself a martial artist, but I also box (I have fought), I do still spar and go to the gym. Most people that know me call me a boxer even though I feel less comfortable being called that than I am being called a martial artist. Thing is, it's more tiresome to correct them, and the point of the correction is lost on so many that I stop trying to. It's easier to say yeah but I don't compete anymore. Most fighters that consistently perform would probably say this about me: "he boxes" but wouldn't call me a "boxer" like them. And you know what, I completely agree with them.
It's kind of splitting hairs in a lot of ways. If someone is really good at sketching, people would call them an artist, but would other artists look down upon that characterization because they have more qualifications and experience being an artist? I know a buddy that plays hockey recreationally and used to be a pretty legitimate player when he was younger. I would call him a hockey player, not "Oh, I know that guy, he used to be a really good hockey player, but now he just plays recreationally". It's easier to say, "he's a hockey player". He will probably spend more time splitting hairs on how accurate that characterization is than anyone would.
I guess it comes down to that line from Joyce Carol Oates, or words to this effect: boxers box (fighter's fight), they do not play boxing.
Because of that it's easier to say you are a this or a that when it comes to sports because anyone can play or do, but you can't say you play boxing or even do boxing. You box, and boxer's box so it seems a bit all encompassing by definition. And because of that, it can be hard to call oneself a boxer unless you are fighitng at that time.
tl;dr: say "I box at a gym, but I don't fight" or "I used to fight/had a fight, but just train now, nothing competitive."
