The short version
Both are external nasal dilators. Intake is premium magnetic with reusability. Breathe Right is FDA-cleared drugstore standard.
When Intake Breathing is the right pick
If you want stronger external magnetic dilation with reusable design and James Nestor endorsement — Intake is the right shape. Premium tier external dilator.
When Breathe Right Original is the right pick
If you want the FDA-cleared drugstore reference at lowest per-night cost — Breathe Right is the right shape. Try this first before committing to premium alternatives.