What kind of vegetarian are you, anyway?

Yes, yes, I know the difference between a traditional vegetarian and a vegan. But until recently, I didn’t know that there were vegetarians who liked meat-free dishes designed to look and taste like, you know, meat. Or, conversely, vegetarians who considered this practice anathema to the very concept of vegetarianism.
I should have known better. Years ago, I was extolling the virtues of an amazing meatless Reuben sandwich sold at the old Manna House Cafe on 95th Street and Nall. It didn’t matter if it was delicious and tasted like the real thing, a vegetarian friend snapped at me. “If it looked like meat and tasted like meat — it was meat!”
Huh?