Here in the states, public school is open to the public, and is paid for by taxes from everyone. Everyone gets to go to public school here.
Private schools are privately owned, and while have government mandated curriculum (largely), they are generally very expensive. This includes religious schools, schools of the arts, etc. Over here there isn's so much of a class distinction between the two. If you are rather poor, you can still apply for a private school grant, and if your child makes good grades, that will also help get you in.
I know this was already mentioned above. Just a Yankee throwing her 2 pennies in. It was confusing to me at first when my British brethren would speak of "public" or "private" schooling.
I went to public school here with everyone else and i dunt think my edewecation suffred much. I are a smart gurl.