I might wish for a new computer. That would be wishful thinking.

I could also pray for a new computer. That would be asking for it (even if the thing I am petitioning has no power or does not even exist).

One could also compare the definitions. According to the American Heritage Dictionary of the English Language, Fourth Edition, it is quite clear that praying involves "God, a god, or another object of worship." Wishing is considered to be a synonym for want or desire.