A dog has two different down positions (more or less).

The alert down

There's the "alert" down where your dog is sitting in a symmetrical position, meaning his front legs are straight out, both of his back legs are in the same position at his sides and facing forward, and his head is straight up and alert. If you're familiar with the Sphinx, he largely looks like that without his nose broken off.

The relaxed down

Then there's the "relaxed" down which is just what it sounds like. It's the position your pup takes when he's most relaxed. For most dogs (but not all), that means he's rolled over on his hip and his back legs are on top of each other pointing to the side. Sometimes his head is up, but other times he might choose to lay his head down on his front paws. When you see your pup in that position with his eyes open, you're convinced he's bored out of his mind and you start to feel a severe amount of pup parent guilt for not designing more fun activities for him, but don't worry, he's fine.

Which down is best?

If you're teaching a long down stay, you shouldn't be concerned about what position your pup chooses and similarly, you shouldn't care if he switches from one down position to another. The success of a long down stay depends on your pup being as emotionally calm and physically comfortable as possible.