I'm by no means an expert and this may be misguided but I think Caribou tend to have a white area towards the end of their snout not present in reindeer, and that's the easiest way to distinguish these animals from the other two animals.
Recently i've started my apprenticeship as a zookeeper in Hannover's Zoo and by chance i`ve been working with this very caribou and it's reindeer companions.
Therefore i can tell by experience that even though they look awfully similar, they can be distinguished first foremost by their size (caribous are remarkably larger), aswell as additionally by their behaviour. Reindeer have been domesticated and are much more tame and trusting, in comparison to the caribou. Even up to a point, where they can be taken on a walk through the zoo with a halter.
Especially noticeable is the behavioural difference while working in the enclosure. While the reindeers are very confident and curios towards one, the caribou always keeps a safe distance, reacting much more timid than the reindeers.
@amur leopard The Caribou depicted in the picture should be "Doris" the last remaining Caribou in Hannover. She lives together with 2,0 Reindeer called "Finn" and "Sven"