fill-column setq-default and add-hook

[Heime]

I want to understand the setting of fill-column.  It is a buffer local 
variable.  

But then there the following possibilities 

   (setq-default fill-column 72)

and       

   (add-hook 'prog-mode-hook  (lambda () (setq fill-column 72)))

The first sets fill-column globally.  What does that mean?  I interpret
that the value is set globally but only to those buffers for which there
is no local binding.  This setting the value (setq-default fill-column 72)
does not always work for the current buffer.  How can one solve this problem?

What does the mode hook do exactly?