“Visit Britain’s only free-ranging herd of reindeer in their natural environment, learn all about them from your guide and walk right in amongst them.”
https://www.visitscotland.com/info/see-do/the-cairngorm-reindeer-centre-p253801
“These tame and friendly animals are a joy to all who come and see them.”
https://www.cairngormreindeer.co.uk/
Those descriptions make them sound like domestic animals. Certainly, tourists would not be encouraged to wander around freely among herds of wild caribou or other large animals [such as elk or pronghorns] in North America.