They should be pronounced the same, the -stan suffix means "land of", "home of" or "nation of".
Pakistan = Land of the Paki's
Afghanistan = Land of the Afghani's
The same applies for Uzbekistan, Turkmenistan, and any number of other countries in that region of the world.
I suspect that Obama pronounces Afghanistan differently because people wouldn't know where he was talking about if he said it in a way that doesn't conform with how the US media has been pronouncing it. It's probably this same reason that the Iraq is pronounced eye-rak rather than ee-rak which is closer to the Arabic, people might think they are talking about another country.