Are stoats the same thing as a ermine?

No they are not, but are in the same family - The ermine or stoat (Mustela erminea) is a small mammal of the family Mustelidae. In North America it is known as the ermine or short-tailed weasel; elsewhere, "ermine" refers to the animal only when it has white fur, which it moults to in winter in snowy parts of its range.

The ferret is a domestic mammal of the type Mustela putorius furo, belonging to the family Mustelidae (weasels)

Source: Wikipedia