It's a common-enough and useful distinction (I might grant that it's something of a false dichotomy, but I think that's besides the point). Just to put a point on it:

"My doctor told me I had two weeks to live, so my church prayed for me to get better, and my cancer went away!"

Tells you effectively nothing about the efficacy of prayer. Multiplying this into a thousand anecdotes also tells you effectively nothing about the efficacy of prayer. By contrast, putting together a good study about the efficacy of prayer with the appropriate controls, tells you quickly that prayer isn't better than chance.