Cone crushers are sort of self explanatory in that the crushing area is conically shaped with a comparable impeller/crushing head. Sort of like a mortar and pestle like compounding pharmacies use.
Impact crushers are hammermill types of crushers. They use a rotor and box crushing area where hammers are rotated on a rotor and material is crushed through the surrounding screens (same principal as an auto shredder).
Jaw crushers or slip jaw crushers, use two articulated heavy jaws that either move side to side or one part is stationary and the other moves, and the material is crushed between the two jaw plates.
They can all be used for aggregate materials, although some work better than others (also personal preference and price enter here). Wood wastes work better through conical (or tub) grinders.
I hope this helps. Let me know if I can help some more.