The questions "Are you already home?" and "Are you home yet?" are similar in meaning, but they have subtle differences in tone and implication.
"Are you already home?"
This question suggests surprise or an expectation that the person might not be home yet. It implies that you thought they would arrive later, but you're checking if they've arrived earlier than expected.
"Are you home yet?"
This question assumes the person is expected to be home soon, and you're asking if they've arrived. It suggests you're waiting for them to arrive but aren't sure if they are home at this moment.
Summary:
"Already" emphasizes something happening sooner than expected.
"Yet" implies you're waiting for something to happen, but you're not sure if it has happened at the moment.