What is the difference between ~ (tilde) and \, (backslash comma) for a nonbreaking space?

The difference between a normal unbreakable space and a thin unbreakable space: \, is 1/6em, while ~ is, if I'm not mistaken, what TeX denotes \fontdimen2, the interword space.

5~kg will not be broken across lines but can be stretched, if needed by TeX: 5 kg. 5\,kg cannot be stretched.