In those two pairs of phrases, 'can't' and 'don't' do indeed have the same meaning.
'Money doesn't buy happiness' = this never happens
'Money can't buy happiness' = it is impossible for this to happen
So, in effect, both sentences amount to the same thing. Likewise, 'I can't understand' and 'I don't understand' : if it's not possible for you to understand something, then you don't understand it.
However, there are, of course, many cases where 'can't' and 'don't' describe different situations. For example, there's a difference between 'I can't drive' and 'I don't drive', or 'He can't help me' and 'He doesn't help me'.