On the basic question
- in jets, the burning of the fuel directly produces hot expanding exhaust that shoots out the back and provides thrust. In addition to whatever mechanical acceleration of air is achieved by blades (fan, compressor).
In jets, the combustion exhaust contribution to total thrust is anywhere from 100% (pure turbojets) to 15% (very high bypass turbofans)
- in prop planes, virtually none of the combustion exhaust produces meaningful thrust (although there have been various experiments and a few somewhat functional attempts to get thrust out of the engine exhaust over the years - cf: augmentor tubes). At best, combustion thrust in propellor engines is about 5% of the total, and usually closer to zero.
Now, in addition to that, you have the differences (as already mentioned) of air inlets, and exhaust nozzles - jets have them, props (except when ducted) don't. And those inlets and nozzles add various effects - such as reducing the onset of shock waves in the air intake, eliminating "sideways" loss of air pressure and thrust, and tightly controlling, shaping and directing the air outflow - the "jet wash".
Consider a fire hose. Put a nozzle on the tip, and you get a much faster and more concentrated flow of water, compared to the rather "sloppy" slower flow you get from a simple hose mouth, even with the same volume of water exiting the hose. The first is a dynamically-controlled "jet" - the second acts more like a propellor - a loose "unfocused" fluid flow, with less speed and effective power.