Cervus elaphusare what we commonly refer to as elk. They also have another common name "red deer". They are indeed the same species with numerous subspecies (Norwegian, Barbary etc).

The major subspecies of Cervus elaphusin North America are as follows:

canadensis - Eastern Elk
roosevelti - Roosevelt Elk
nannodes - Tule Elk
nelsoni - Rocky Mountain Elk
merriami - Merriam elk
manitobensis - Manitoban elk

Merriam(TX, NM, AZ)and Eastern (Penn, Ontario?)are thought to be extinct.

Manitoban are not extinct.

I don't know any white elk. I can look in my mammal book.