Someone attempted to argue with me that vanilla ice cream is "spicy" because vanilla is a spice. While pedantically true, that's not a person I'd ever want to eat dinner with.
But it is an annoying ambiguity in English. You would probably say that curry paste is spicy even it had no capsaicin, which does happen. People also mean "has spices" when they say "spicy". I have heard Russians use the word Russian word "bitter" to describe the pain sensation of capsaicin too.
I prefer the Spanish word "picante" - stingy. It stings, it causes pain. It's not a flavour like a spice would be.
The problem is that there just isn't a good English word to distinguish it, I have to explain every time that I don't mean flavour, I mean pain. (Russian also has this problem, ambiguity is in every natural language.)
I have heard older Soviet Russians use the word горко, but this was about ten years ago. They were trying to express that the food tasted bad and they really just called it bitter when they meant it had capsaicin.