Both, and the reconciliation is that focal length changes where you stand.
Perspective, meaning the relative size of near and far objects, is determined by camera position alone. Shoot the same scene from one spot at 24mm and at 200mm, then crop the wide shot to match: the perspective is identical.
What actually happens is that nobody does that. To fill the frame with a face at 24mm you must come very close, and at close range the nose is meaningfully nearer the lens than the ears, so it renders larger. At 85mm you stand back, the distance ratio between nose and ears shrinks, and the face flattens.
So the lens is not distorting anything. It is changing the distance you shoot from, and distance is what does it.