The meat from any deer is venison. That is then broken down into deer meat, elk meat etc. But only if you wish to be correct. When a consumer buys commercial "venison", there is no gaurantee it has come froma whitetail or even a deer. Quite often, it is all lumped together with other varieties. That is especially true of New Zealand meat. A lot of it is commercially grown red deer.
Oddly enough, I was just in a discussion about this with a couple federal guys,four days ago.