ARE THIS SAME MEANING FATE AND MATCH
Bush and his criminals have finally met their match
BUSH AND HIS CIMINALS HAVE FINALLY MET THEIR FATE
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No. There is no relation between the two words. ‘Match’= equal in ability/power/etc.
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No, the phrases have different meanings.
The first - met their match - implies that Bush et al have encountered ‘someone’ who is equal or better than them (in some contest - the political arena for example). It is usually used when someone has been a leader in a field (often in sporting context) and is finally beaten.
The second - met their fate - indicates that they have received an outcome that has ‘always’ being coming to them (as a result of their actions).