That is indeed correct! On the Department of Defense photo pages, the pictures of the Constitution formerly bore a legend such as "The U.S. Navy’s sailing ship USS Constitution, the world’s oldest commissioned warship, . . . " The HMS Victory is, I believe, still afloat, but I do not know if it is actively commissioned, or whether it is only a museum. I also don't know whether it is capable of sailing at this juncture. Constitution ventures out at lest once a year.
USS Constitution under sail in Massachusetts Bay, 21JUL97
Nos genuflectitur ad non princeps sed Princeps Pacem!
Listen, O isles, unto me; and hearken, ye people, from far; The LORD hath called me from the womb; from the bowels of my mother hath he made mention of my name. (Isaiah 49:1 KJV)