The vaccines are the same and their indications for use have not changed but the FDA has given full approval to the Pfizer vaccine for patients 16 and up, while the Moderna and J & J vaccines are still covered under emergency use authorization. 

One would hope that full approval could reassure anyone holding out from an “authorized” but not fully approved, “experimental” treatment, since a vaccine’s full approval requires more safety data than its emergency authorization. More employers and organizations may be more willing to enact vaccine mandates for a fully FDA-approved vaccine. Also, doctors have the discretion to use fully approved medications as they see fit, including “off label” use different than the FDA-approved stipulations (such as for children or as off-label boosters); whereas, the government prohibits off-label uses for EUA (emergency-use authorized) treatments. Finally, Pfizer gets to pick a brand name rather than us referring to it as “Pfizer vaccine”. It will now be known as “Comirnaty” (silly name, IMHO), with the accent on the “mir”. 

Moderna submitted for full FDA approval about a month after Pfizer, and J & J plans to submit soon. Because EUA’s are only granted when there are no fully approved alternatives, there is a possibility that EUA for Moderna or J & J will be withdrawn if they don’t hurry. 

— via Lifehacker

What I don’t know is the impact this will have on use of the vaccines outside the US.