坐

坐下 adds 下, the same 'down' you see in 下来, so it describes dropping into a seat. 坐 alone just describes being seated, or sitting in general. That is why a host waves you toward the sofa with 请坐, while a doctor points at the chair and says 请坐下. Use 坐下 when you want the person to actually move and plant themselves.

Chinese stacks the trip in order: how you travel first, destination second. So 我坐飞机去北京 means the flight carried you to Beijing. Flip the two, and 去北京 becomes the purpose of the whole trip. Anyone hearing 我去北京坐飞机 pictures you heading to a Beijing airport to board a flight. Same logic works for 坐火车回老家 and 坐地铁去上班.

坐 names the action, and 在 pins down the exact spot, so the two stay glued as 坐在 plus a place. That gives you 他坐在地上, 别坐在桌子上, 我们坐在窗边. In fast speech people simply drop 在 and keep 上: 你坐沙发上, 你坐这儿. But 他在椅子上坐 leaves the listener hanging, waiting for the rest of the story.

Chinese treats riding as sitting inside the thing, so 坐飞机 means taking a plane. The same verb handles 坐火车, 坐地铁, 坐出租车, even 坐电梯. It stops at anything you straddle or work with your own legs: a bike is 骑自行车, and on foot you 走路 or 走过去. Think 'seated passenger', not 'driver of a vehicle'. “从北京到上海坐飞机，不到两个小时，但是要坐火车，就要最少五个多小时。” (Flying from Beijing to Shanghai takes less than two hours, but if you take the train, it takes at least five hours or more.) ── [《去上海》](/read/train-or-plane-to-shanghai#s7)