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Reciprocating engines have pistons, while jet engines do not. 

Piston engines have been used on airplanes since the Wright Brothers' days. They work by bringing air in in one stroke and building its pressure, which turns a propeller.  While very heavy duty, piston engines aren't usually used on high performance aircraft, such as today's comercial airplanes. You usually see them on small planes with propellers.

Jet engines use combustion (created by a chemical reaction which is ignited) to thrust forward. They are used on comcercial airplanes and on military planes.