If someone takes a picture of you (without your permission), who owns the picture?

There is a difference, but as @bdgr notes, the distinction in the United States is a bit more complicated than that.

As this suggests, the issue is not whether or not the photographer makes a profit from selling the photo; the issue is what particular purpose the photo is used for.

A photographer taking a picture of people gathering in the park on a sunny day could sell it to a newspaper seeking to illustrate a story about the great weather in the city over the weekend, but could not sell it to a pharmaceutical company seeking to use it for advertising sunscreen.

Or rather, the photographer could sell it to the pharmaceutical company, but without a model release they’re not going to be able to use it in an advertisement.

There was actually an interesting case about this sort of thing a few years back. The recording artist Bruno Mars and his record company posted, on his official Instagram page, a picture of him as a kid. The picture had been taken, back in 1989, by a professional photographer.

Despite the fact that the photo was of Mars himself, the photographer sued Mars and the record company for copyright infringement. The suit ended up settling out of court, mainly because Mars and the record company didn’t have a leg to stand on.