The short answer
Slabjacking is a broad term for raising concrete by pumping material beneath it. Mudjacking is a traditional slabjacking method using a pumpable slurry.
Slabjacking = broader process
Mudjacking = slurry-based slabjacking
Polyjacking = foam-based slabjacking
Search terminology overlaps heavily
Common questions
Are mudjacking and slabjacking interchangeable?
In everyday contractor language they often are, although slabjacking can also refer to other injected materials.
What term should homeowners search?
Concrete leveling, concrete lifting, mudjacking, slabjacking and polyjacking can all lead to relevant contractors; the important step is confirming the actual method proposed.
Use this information to compare quotes
Ask each contractor what material will be injected, how the original cause of settlement will be addressed, what is included in patching and cleanup, and what conditions are excluded from any warranty.