Is aristocracy and bureaucracy different

In theory, they should not be different, but in practice they are. Aristocracy literally means 'rule of the best'; bureaucracy is a system where rule is done by appointed officials who generally are well-trained in their field (good training is also called 'merit'). In theory, aristocracy should be meritocracy (which means rule by those who are best qualified) as bureaucracy usually is, but in history, aristocracy is associated with rule of the nobility and privileged who earn their position not by ability but by birthright. In some countries too (i.e.) former communist countries) bureaucrats also exploited their positions to attain things they did not earn. But in general, yes, the two are different but they technically should not be.