sleep() is a blocking operation that keeps a hold on the monitor / lock of the shared object for the specified number of milliseconds.

wait(), on the other hand, simply pauses the thread until either (a) the specified number of milliseconds have elapsed or (b) it receives a desired notification from another thread (whichever is first), without keeping a hold on the monitor/lock of the shared object.

sleep() is most commonly used for polling, or to check for certain results, at a regular interval. wait() is generally used in multithreaded applications, in conjunction with notify() / notifyAll(), to achieve synchronization and avoid race conditions.