Balloons float because they are lighter than the air around them, so they try to float on top of the atmosphere just like a boat floats on top of the water. Since they float, they are at the mercy of even the slightest breeze or change in air pressure.
Rockets are heaver than air, so they have to overcome gravitational pull and air resistances by creating their own thrust. Since they create their own thrust, they can change the angle at which the thrust is emitted (Thrust vectoring). This allows them to keep the rocket stable during flight by aiming the thrust.
Older rockets, and rockets that need high maneuverability (Mostly military missiles) will use fins to direct air flow just like airplanes do. Thrust vectoring isn’t strong enough to make sudden maneuvers. The reason space rockets don’t use fins anymore is that they create drag and add to the complexity of the system, thrust vectoring is all they need as they don’t do sudden maneuvers.
The nozzle on a balloon is floppy – it flops around all chaotically as air wheezes out of it. The exhaust bells on a rocket are on gimbals – on giant motorized mounts that can aim the thrust coming out. Then, the problem becomes how do you balance a broom on your hand (aka the so called inverted pendulum), but as it turns out we have really good computers that have already solved that problem.. so [much so that you can easily do it at home](https://www.youtube.com/watch?v=nxRWKAauAMo) with a cheap computer and some spare parts.
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