What does a rocket nozzle do?

Hot gas in the chamber is pushing in every direction at once. The nozzle gives it one way out and shapes how it leaves. Narrow first, at the throat, then widening into the bell.

That shape matters more than it looks. Gas leaving faster produces more thrust for the same amount of propellant, and the expanding bell is what accelerates it. This is why nozzles are the shape they are rather than simply being a hole.

How wide the bell should be depends on where the engine is used, which is why the two ends of a Falcon 9 look so different. The nine sea-level Merlins have short bells, because a bell too wide for thick air actually loses thrust. The single engine on the upper stage never sees thick air, so it carries a huge bell with an expansion ratio of 165 to 1 — and gets 348 seconds of specific impulse out of the same fuel, against 282 at sea level.

Same propellant, same basic engine, better nozzle for the job. That difference is worth an enormous amount of payload.