More or less. Every airport has a traffic controller whose job it is to coordinate different planes operating around it. A typical airport has “lanes” that planes join until cleared to land or that they follow after takeoff.
Away from an airport, the sky is just so big that there’s not *that* much coordination required. There are a matter of a few thousand flights in the air in the US at any given time – let’s say 5,000 for a nice round number (the FAA says that’s [close to peak activity](https://www.faa.gov/air_traffic/by_the_numbers/)). Dividing the area of the continental US by that number tells us that each plane has an area [about half the size of Rhode Island](https://www.wolframalpha.com/input/?i=3%2C119%2C884.69+square+miles+%2F+5%2C000) to itself. So there’s not much risk of a collision, particularly when you keep in mind that they also have a mile or two of vertical room to play with (and once there’s only a few planes around, a pilot can reasonably keep track of them all).
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