"TWO Endings"
just fyi, there are at least* SIX endings + a secret cutscene
(*might be even more)
SPOILERS Below
Secret Cutscene (Fail the Golden Puzzle and plummet to your death)
King Ending A (Finish the Game)
King Ending B.1 (Go Right on the End)
King Ending B.2 (Free all Foxes and go Right)
Sacrifice Ending (Get Caught and diffuse Missiles)
Ouija Ending A (Don't diffuse Missiles, say "YES" or "NO + NO")
Ouija Ending B (Don't diffuse Missiles, say "NO + YES")
Edit to add: After you diffuse the missiles, you cannot fail. When the €uropean reaches you, he just goes past you and leaves the screen. Doing the orbital, he's just at the end of the hallway again.