I just say 'I don't eat meat' or 'Put me down for the veggie option'.
I went vegetarian in the early 80s, as a young teenager. If I were deciding now, tbh, I'd probably feel I could be more effective in influencing farm animals' welfare by continuing to eat meat, but being bloody fussy about its provenance.
Again - it seemed OK to me to eat fish, back then, because AFAIK it wasn't being kept in some horrible concrete crate full of shit. Hmm. So now I don't eat farmed salmon.
So, if you slapped a big juicy steak down in front of me, having been on first name terms with its organically-reared & humanely-slaughtered provider, I'd have no ethical problems with eating it - I'd just feel sick at the prospect, given that I haven't eaten a chunk of dead cow in 25 years!
I suspect that 'vegetarian', 'pescatarian' etc are terms that are going to be less & less used, tbh, as people have more choice & more consumer power re: how their meat is produced.
& also as vegetarian meals become more & more mainstream - I don't think my dad had ever sat down to a meatless meal before his 50s; he now routinely cooks vegetable curries, or makes a veggie version of lasagne, & saves meat-eating for steaks & roasts.
The only place where I see it as a problem, is if you're a vegetarian captive audience eg. in hospital, & someone's trying to tell you that fish fingers are today's Vegetarian Choice. But anyone working in catering ought to make it their business to know better than this!