The short version
Headspace teaches meditation; Calm provides ambient wellness content that includes meditation. Both work; the right pick depends on whether you want to learn or to consume.
When Headspace is the right pick
If you have never meditated and want to learn — the Basics course, the structured curriculum, the consistent teacher voice — Headspace is the right shape. The library is narrower but deliberately so; the value is the teaching quality, not the breadth.
When Calm is the right pick
If sleep content matters as much as meditation, or you respond better to celebrity narration than to a single teacher voice, Calm is the right shape. The library is broader, the Sleep Stories format is category-defining, and the ambient soundscapes work as background content in a way Headspace does not.