As msoebel said, it's a prayer shawl if you call it a prayer shawl, and if you want it to be a prayer shawl. You can consider that it's got your prayers for the person receiving the shawl knitted right into it.
Some people do the prayer shawl thing with spoken prayers over the person receiving it -- which may or may not be to everyone's taste. Other people do their prayer shawls "anonymously," you might say -- praying for the wellbeing of whoever receives the shawl, no matter who it is and they may not even know the recipient. There are a lot of ways to do prayer shawls.
You don't even have to call it a prayer shawl for it to carry your good thoughts for the person. You might make a shawl for a friend & call it a friendship shawl. Or you could just knit it up, thinking good thoughts about someone the whole time, and call it "the shawl I made for you just because."
(I've got one of those on the needles right now.)