I should clarify, when I'm saying "jet", I do mean turbofans. And turbofans still include a jet engine, but the output turns a turbine which rotates the fans.
Turbojets, turbofans, and turboprops all use gas turbines. The "jet" in this context refers to the action of the exhaust, not the mechanism creating the exhaust (which is the gas turbine.) Turbojets and Turbofans both create jets of hot exhaust gas to produce thrust. Turbojets produce thrust exclusively with this jet of exhaust gas, while turbofans produce some [often most] of their thrust by using some of the turbine's output to turn a ducted fan. Turboprops don't produce any meaningful jet of exhaust gas, instead using the output of the gas turbine to turn a propeller.
Related to turboprops are turboshaft engines, which turn a power transmission shaft instead of a propeller directly. In some cases, like the V-22 Osprey, the line between a turboprop and a turboshaft is blurred. But some clear examples of turboshaft engines are in modern helicopters and Abrams tanks.
There are some kinds of jet engines that don't use turbines. Ramjets and scramjets don't use turbines, but have 'jet' in the name because they produce their thrust using a jet of hot exhaust gas. Rocket engines produce jets of hot exhaust gas, but aren't called jet engines because.. reasons.
> jet: A collimated stream, spurt or flow of liquid or gas from a pressurized container, an engine, etc.
(Note that this makes turboprop engines not jet engines, but turbojet and turboprop engines are both gas turbine engines.)