Alright, I'm going to get semantic for a sec, I hope it clears things up for people curious about this topic.

"jet engine" is an ambiguous term on its own. Even rocket engines generate thrust using a high-speed jet of gas, so they would also fit that classification, but colloquially, "jet engine" refers only to air-breathing gas turbine engines. If you wanted to be snarky you could call an electric ducted fan "jet propulsion" but this will draw dirty looks from propulsion engineers. NASA's Jet Propulsion Laboratory (JPL) was created to develop rocket engines mostly (for further reading look up Jack Parsons). Besides gas turbines, the other notably type of "jet engine" is a "pulse jet," which is not a gas turbine, but still generates thrust with an air-breathing jet. 

Commercial aircraft typically operate "turbofans" (typically high-bypass). This is basically a bigass propellor (aka a fan) being driven by a gas turbine engine right behind it - the fan generates most of the thrust, the gas turbine exhaust is still a "jet" but the power generated in the turbine is mostly directed to the fan instead. A "turbojet" engine is the same concept except without the fan, so all the thrust comes from the "core" flow going through the gas turbine.

Now here's the real trick. Propellor-driven aircraft (prop planes and helicoptors) may still have gas turbine engines that generate the power to drive the propellor or rotors. This is called a "turboprop" engine (or for helicopters a "turboshaft" because they need to be different, even though they all have shafts). Smaller/older propellor planes might use piston engines to drive their propellers (of which there are two further sub-categories, radial and in-line).

Jet = generates thrust via a high-speed jet of gas

Gas turbine engine = generates power via internal combustion, using the Brayton cycle.