Hot peppers are distinguished from sweet peppers simply by their pungency or hotness of flavor. There are thousands of hot pepper varieties in the world. (This is the case because peppers easily cross pollinate to produce new kinds.)
The hotness of a pepper is determined by number of blisterlike sacs of capsaicinoids on the interior wall of the pepper. Capsaicinoids are organic chemicals. The more sacs of capsaicinoids the hotter the pepper.
Hot peppers go by several names. Most commonly hot peppers are called chili peppers in the United States. 'Chile' is Spanish for pepper. In Mexicochile dulce is a sweet pepper, chile jalapeño is a jalapeño pepper. When the name chile first came to the United States it was used to mean different kinds of peppers in different parts of the country. In time, the spelling "chile" was eventually corrupted to "chili" and the term came to be commonly used to describe any pepper that was hot flavored.