A Caribou is the same thing as a Reindeer.

in North America it's called a "Caribou"

A Caribou IS a Reindeer. The confusion may have arisen because the use of reindeer as a Christmas symbol originated in northern Europe, where almost nobody uses the word "Caribou". If the tradition had started in Alaska, Santa's sleigh might have been pulled by eight Caribou.

The Caribou is a member of the deer family, living in the northern regions (like the North Pole). Unlike other deer, Caribou of both sexes have antlers. Like other deer, they are herbivores - meaning they eat plants. They have extraordinarily thick and buoyant coats, enabling them to live in extremely cold weather, and actually sleep while floating in water.

There are millions of Caribou/Reindeer in the world. Almost all species
migrate twice a year, following safe and trusted routes they've taken every spring and fall for centuries that are about 600 to 800 miles long. (They walk or run, not fly) .  On migratory trips, the adult females leave about two weeks before the rest. The males and juveniles leave later.

Merry Christmas!!

Partidge in a perdrix?       The Christmas quote about a “partridge in a pear tree” could possibly have been a simile, pun or mistranslation, according to John Riutta, in Backyard Birds Newsletter.  The tale, having wound itself through many languages and cultures may have borrowed from the French.  The French word for partridge is “perdrix” (pronounced something like “pear-dree”).  This sounds suspiciously like “pear tree” in English.  Maybe the long-forgotten author of the song was focusing on a single partridge in a tree full of partridges. Who knows?