You are not missing anything. You are correct.
Not entirely; the Tridentine (’old’) mass is ‘offered.’ The priest ‘says’ mass or ‘offers’ mass. Lay people in the church ‘assist’ at mass (’active participation’ on the spiritual, not physical, level). ‘Celebrate’ is the newer description and, arguably, incorrect.
If I’m wrong, there are a few good experts here on liturgy history whom I invite to correct me! Very few people under age 55 know these details and the reasons.