The European Reindeer and American Caribou are the same thing. Reindeer comes from the Old Norse word "hreinin," which means "horned animal." Caribou is based on the French word for "snow shoveler," in reference to the animal's habit of digging through the snow for food.
Clement C. Moore's poem, "A Visit from Saint Nicholas," which first
introduced the world to Santa's reindeer, describes them as tiny. The only reindeer that could really be considered tiny are the Svalbard subspecies, which weigh about half as much as the average reindeer species and are at least a foot shorter in length - that definitely proves useful when landing on roofs.
Strangely, you'll almost never see these guys in depictions of Santa, as live-action films usually use full-sized reindeer and animations usually draw the creatures as a cross between a regular deer and a reindeer.
While human vision cuts off at wavelengths around 400 nm, reindeers can see up to 320 nm. This range only covers the part of the spectrum we can see with the help of a black light, but it is still enough to help reindeer see things like white fur in high contrast that they would otherwise miss against the glowing white of the Arctic.
facts gleaned from mentalfloss.com