How exactly does the Double Jeopardy rule work?

I know that a person can't be charged for the same crime twice, but that also confuses me. Like, if a person tries to murder someone but fails, they get charged with attempted murder. Say they get acquitted and try to murder the person again. If they fail again they can't be charged, right? But if they succeed they can be charged for murder because attempted murder and murder are different charges?