Transit through Beijing airport

I just want to make sure I understand this. I have a long, less than 1 day layover at the Beijing airport before going to my next country. And I have a layover in Beijing of less than 1 day on my way back to the US where I would love to leave the airport. So, with a USA passport and these situations, I don't need to apply for a visa to China, correct? I will go to the correct window at immigration and will then get to leave the airport right away, not have to wait until midnight. I am hoping this is correct as this would be my best case scenario.

Thanks!