In original usage, an engine was any sort of mechanical device. The term "gin" in cotton gin is a short form of this usage. Practically every device from the industrial revolution was referred to as an engine, and this is where the steam engine gained its name. This form of the term has come into use again in computer science, where terms like "search engine", "3-D graphics game engine", "rendering engine" and "text-to-speech engine" are common. The earliest mechanical computing device was called the difference engine; Military devices such as catapults are referred to as siege engines.
In more recent usage, the term is used to describe devices that perform mechanical work, follow-ons to the original steam engine. In most cases the work is supplied by exerting a torque, which is used to operate other machinery, generate electricity, pump water or compress gas.
In the context of propulsion systems, an air breathing engine is one that uses atmospheric air to oxidise the fuel carried, rather than carrying an oxidiser, as in a rocket. Theoretically, this should result in a better specific impulse than for rocket engines

AoA

Sorry brother, the rocket engine is a non-breathing type. The breathing type cannot be used in space. The term breathing type engines refers to the engine like jets and trbines. They operate on an intake of air and then the volume of air is increased rapidly by heating by the virtue of fuel ignition. The heated up gas expands and escapes out from the other end. This escaping air is used to eihter move the propeller or impeller (whatever might be the case). In the rocket engines, liquid hydrogen and oxygen are the intake fuels, contained in respective reservoirs (Cylinders) and are given ignition at the base point, producing an oxy-hydrogen flame which produces about 4300 degrees celcius (The highest combustible temperature so far of any fuel).
So, as u see that there is no intake of air from the environment, so it is called a non-breathing type.
Hope that u understand.

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@ Sohail Shuja
Sorry but the above article never says that the rocket engine is the air breathing type of engine.

@ Gr8khali
Nice contribtion bro. But the rocket engine is more efficient in terms of power production. The air breathing type is just more cost effective.
The broad categories of mechanical engines are combustion engines and the non-combustion engines.
The non-combustion engines do not use combustion as in the compressed air engine and the gravity engine.
The combustion engines are divided into two broad categories of internal combustion engines and the external combustion engine.
One of the upcoming types of external combustion engines is the breathing rocket engine, which breathes the oxygen from the atmosphere as long as it is in the atmospheric bounds. Afterwards and beyond, it is the same old Oxy-Hydrogen rocketry. This modification is done in order to reduce the cost of fuels used and thier amount also.
The future popular type of internal combustion engine is the rotary wrankle or commonly called the "wankie" engine. It does not use the conventional pumping type pistons, rather, it uses the rotary pistons to move the crankshaft. This type of engine is more fuel efficient and less in size, weight and parts. Moreover, it is a "knockless" or no vibration engine. Mazda has introduced it Rx8 in this technology, while the ever first bike with such technology was introduced by "Norton" back in 1990's