So, the "Do Re Mi" is a great launch for an example of a scale and key. As you step through it singing, each sound is a slightly and particularly higher note than the last right? If you do it again, but sing the first Do at a different starting note (lower or higher, doesn't matter) you'll step through the rest of that scale on the same pattern of rising notes. So here, you're singing the scale in a different key. Same sounds, same pattern, but different "base" note.

Songs are all in a key, that is rooted in a base note and a particular pattern. Another artist might play the same song in a different key for a stylistic reason or simply a preference. Like the cover versions of Landslide or Jolene.

An easy place to hear a key change is in a lot of older country songs, like Good Hearted Woman. That song is in one key for most of it and then transposes up a bit to a new key. They play the same pattern, but base it off a different key.