It doesn't work THE SAME. Which is why all rockets have stages: one for use within the atmosphere, and one for use outside of it.

It's not so much thermodynamics but the uh was it archimedes who first said, "any force exerted on a body engenders an opposing, equal force on that which pushes?" or somesuch. Basically, it's the exhaust from a rocket which pushes against the rocket nozzle, which creates the momentum. It's not "pushing on air" although obviously that helps a little while moving through the atmosphere, but it also helps brake the forward motion of the rocket. This is only valid for a combustion-based engine, however.

There are new engine technologies being developed for actual interplanetary travel which don't rely on combustion: firing a stream of particles at a VERY high speed provides thrust in the opposite direction. That's the conservation of momentum: by accelerating relatively light particles at very high speeds (near the speed of light) in one direction, the relatively heavy spacecraft gets a tiny amount of thrust in the opposite direction. This is the nuclear thruster technology, which expends very little matter, meaning it can go on thrusting for very long periods (years!) at low accelerations, but in turn, will keep providing thrust even at very high speeds.

Needless to say, such a thruster would only be useful for long trips outside of the intense gravitation of planets' neighborhood.

Think of it this way: you stand in a rowboat with some rocks in it. The water is perfectly still. The boat isn't moving. You throw a rock as hard as you can, horizontally, in the direction of the back of the boat. Does the boat stay still? Nope, it starts moving forward. You can do this with heavy rocks (they won't move very fast or go very far) or with small rocks (they will go much faster and further) and you can find the size rock that suits your physiology best at producing the most momentum for your boat. No need for oars. ;-)