As The Nibble correctly observes:
“Chile pepper” is a misnomer, and the term “pepper” is not used in Latin America.
Unfortunately for me, I am one of those people who have been using the term “chili pepper” without caring how terribly incorrect the phrase is and even while knowing that the chili and the pepper are two different plant species. But the nice thing about learning is that mistakes don’t have to be repeated. Henceforth, if I mean chili, I’ll say chili. And if I mean pepper, I’ll say pepper. No more references to the non-existent chili pepper.