It's a lot easier to be vegetarian (and vegan) in Israel. If a restaurant is "milky" (as my husband says) they don't have meat anyway so it's a lot easier to find vegetarian dishes and unlike in the US they don't smother everything with cheese so it's easier to find fully plant-based dishes too.
It's common issue of language learners to over estimate the speed. https://www.psychologytoday.com/us/blog/life-bilingual/201302/why-are-they-talking-so-fast
Actually, there is a difference. Vegetarian in English can be both an adjective and a noun. If it's a noun, if it's singular then it gets "a". Only then. However here it's an adjective, in plural form, and adjectives don't get articles when they stand on their own, not to mention when they are in plural, like here. So no, "a vegetarian" is not correct here.