They almost mean the same thing and most of the time, they can be switched with each other. The difference is cultural. If I go out for a walk, the image is one of walking for a half-hour to maybe two hours. The time would be limited. If I say I'm going walking, it would mean the same as "go for a walk", but it could also mean a very long walk - a whole afternoon perhaps. Also, if I am walking in the forest or in unpopulated country, we would call it 'hiking'.