Is a lavender oil capsule different from aromatherapy?
Yes -- the anxiety evidence concerns a specific standardized oral oil capsule (Silexan), a different product from lavender tea or aromatherapy, which haven't been studied to the same standard.

The short answer
A 2017 meta-analysis of 5 studies (1,165 participants with diagnosed anxiety) found the standardized oral lavender oil preparation Silexan significantly outperformed placebo for anxiety symptoms, with a tendency toward an even larger effect in generalized anxiety disorder specifically. This is a pharmaceutical-grade oral capsule, genuinely distinct from culinary lavender, dried flower tea, or aromatherapy essential oil use -- those forms haven't been studied to the same rigorous standard, even though lavender has been used across Mediterranean and European herbal and aromatic tradition for centuries. Oral lavender tea or extract may cause headache, appetite changes, or constipation, and can increase drowsiness combined with sedative medications.