Let me answer this question once and for all. Is a reindeer the same thing as a caribou? The answer is...yes...and no. It's sort of a chicken or egg situation. Only it's not, because there's a definitive answer.
Caribou, a member of the deer family, evolved in North America--specifically, what is now Alaska and the Yukon--and spread eastward. All the way eastward to Europe and Asia, where they are known as reindeer. Potato, patahto. This whole migration took place before the last glaciation of our planet. We're talking about a world where Europe, Asia, and Alaska are still connected. Think big here. 21,000 years big.
Caribou and reindeer are the same species, yes. But, they are vastly different subspecies genetically and would not interbreed well. Because of their differing environments, they are two different beasts.
The caribou that live in almost all Canadian provinces (including Newfoundland, where I live) are called Woodland Caribou. They survived the Great Ice Age and moved into much of Canada for good ~10,000 years ago.
The original caribou, the herds that live in Alaska northeast to Baffin Island, are called Barren-ground Caribou. There is one other subspecies called the Peary Caribou that lives only on Canada's Arctic Archipelago. And then, of course, there are reindeer.
Hopefully that cleared things up.
A quick note on antlers. The magnificent rack of antlers seen on male and female caribou grow from nothing and fall off every single year. Male caribou grow a much larger and more complex set of antlers than females starting in March every year (female antlers begin growing in May). Antlers bear a soft, fuzzy tissue called velvet during development. This tissue is basically a protein shake (more like continuous supply of blood and nutrients) for the antlers beneath as they grow and harden. Caribou (and other deer species) rub the velvet off on trees and rocks when the antlers are fully grown. A male caribou starting with tiny nubs of velvet in March may have 3-foot-long fully developed antlers by August. Just in time for mating.
Antlers fall off in late fall after the rut (breeding season) for males. Females keep their antlers until after they calve.