Take for example, the species Capsicum frutescens; members of this species can be annual or short-lived perennial plants. Flowers are white with a greenish white or greenish yellow corolla, and are either insect- or self-pollinated. The plants' berries typically grow erect; ellipsoid-conical to lanceoloid shaped. They are usually very small and pungent. Note the very use of the words, "can", "frequently", "typically".
Another species is Capsicum annuum. This species is the most common and extensively cultivated of the five domesticated capsicums. The species encompasses a wide variety of shapes and sizes of peppers, both mild and hot, ranging from bell peppers to chili peppers.
Further still, the species Capsicum chinense describes the Habanero pepper. As a very separate species unto itself. Native to Central America it was incorrectly assumed that it was a chinese pepper and so carries the Latin designation naming it the "Chinese Pepper".
While the latin naming of capsicum peppers can be confusing when it tries to be specific, what really drives people crazy is renaming a pepper when the fruit is dried.. The Poblano pepper, a nice large and mild pepper is called Chile Ancho (Wide Pepper) when dried. The jalapeno is smoke-dried to become a Chipotle.
The chile pepper as opposed to a chili blend. English is not the only language with homophomes. Both nouns, chile referrs to the plant and fruit thereof; chili, on the other hand, is a dish served hot. In many parts of Asia and India, Chilly or Chilli is the preferred spelling of the plant and all it's variations.
However you spell it, it all sounds good.