They are not semantically equivalent.
Suppose you have no idea who Hitler's Minister of Propaganda was. If asked, you should say, 'I don't know,' not 'I'm not sure.' If, on the other hand, you think it was Joseph Goebbels on the basis of a history course taken long ago, then 'I'm not sure' is appropriate.
'Not sure' implies some knowledge of the subject matter but not enough to justify one's being, well, sure. 'Don't know' lacks this implication.