
The principle of operation of the rocket engine (refer to Figure 1) is divided into three main components and differs slightly with the type of propellant used. First is the propellant combustion or heating, which produces exhaust gas. Then it is passed through a supersonic propelling nozzle, which helps to accelerate the exhaust gas to high speeds using the heat energy of the gas itself. Then the engine is pushed in the opposite direction, as the reaction to the exhaust flow.

Jet engine consists (refer to Figure 2) of many parts such as a fan, compressor, combustor, turbine, mixer, and nozzle. The engine sucks the air and compresses it into the compressor. Then the compressed and heated air is sent to the combustor and mixed with fuel and burn. The exhaust is sent to the turbine to produce the thrust to drive the engine.
Apart from this, the finer points of difference do exist. Firstly, jets get the oxygen to burn fuel from the air and hence cannot operate in the vacuum of space. Whereas, rockets carry their own oxygen (oxidizer), which allows them to operate in space. As a rocket enjoys the luxury of being fed propellant and oxidizer at just the right ratio, condition, and at high pressure, and since the oxidizer is mostly pure liquid oxygen, the turbopumps for compressing it can be much smaller than the turbomachinery of a jet which works with an ~80% nitrogen – ~20% oxygen mixture of gasses.
Secondly, both engines burn fuel at different rates. For example, Saturn V’s first stage carried 205,400 gal/770,000l of kerosene fuel, which is burned in a bit less than 3 minutes. Whereas, a Boeing 747 carries about a quarter as much (48,445 gal/183,380 l), and burns it over perhaps 12 hours.
And lastly, jet engines have two openings (an intake and an exhaust nozzle) as compared with rocket engines having only one (an exhaust nozzle).
Now comes a question, what would happen if rocket engines’ propulsion system is present in the airplanes, please mail us the positive and negative aspects of it? We would love to discuss the same with you.
References:
https://en.wikipedia.org/wiki/Rocket_engine#/media/File:RS-68_rocket_engine_test.jpg
https://www.differencebetween.com/difference-between-jet-engine-and-vs-rocket-engine/
https://www.isro.gov.in/launchers/isro%E2%80%99s-scramjet-engine-technology-demonstrator-successfully-flight-tested
https://aviation.stackexchange.com/questions/23942/how-do-rocket-engines-produce-more-thrust-than-aircraft-jet-engines
https://jalopnik.com/suck-squeeze-bang-blow-ge-explains-how-a-jet-engin-1593409462
https://howthingsfly.si.edu/ask-an-explainer/what%E2%80%99s-difference-between-jet-engine-and-rocket-engine http://barriosengineeringportfolio.weebly.com/uploads/1/6/6/5/16650342/3393920_orig.jpg
https://anjungsainssmkss.wordpress.com/2011/09/20/comparison-between-jet-engine-and-rocket-engine/