Correct. From the FDA doc:

On August 23, 2021, FDA approved the biologics license application (BLA) submitted by BioNTech Manufacturing GmbH for COMIRNATY (COVID-19 Vaccine, mRNA) for active immunization to prevent COVID-19 caused by SARS-CoV-2 in individuals 16 years of age and older.

BLA Approval = FDA Approval

From FDA's site:

https://www.fda.gov/vaccines-blood-biologics/development-approval-process-cber/vaccine-development-101

By submitting a BLA to the FDA, a company is seeking permission to distribute and market a vaccine for use in the United States. FDA evaluates the data to determine whether the safety and effectiveness of the vaccine has been demonstrated and whether the manufacturing and facility information assure product quality and consistency. After its evaluation, FDA decides whether to approve (also known as to license) the vaccine for use in the United States. If FDA approves the vaccine, the company is permitted to market it in the United States for use in the population for which it is approved.