It's a minefield of ambiguity which a new word could easily solve. It could well be, as you say, it's only recently that hot spices have become mainstream.
I grew up in the 1960s & 70s in northern England and as a kid my parents may put some very old pre-ground pepper on the table occasionally. Garlic didn't exist to us. I burst out and enjoy hot, bitter, gnarly flavours.
The closest I think in English is how we have modified the word "spice" to be, in context, "spiced" vs "spicy".
The former implies the "herbs and spices" and the latter the "hot pepper" types. But it's not exactly consistent.
We of course have the modifier "hot" which works. And we stole piquant from the french, but that is a little different I think.
I've also heard foods described as having "bite" to indicate that they have a strong, spicy flavor, but not necessarily a "hot" one.
That's not currently a real English word. But it could be!