Emptying and cleaning are closely related, but they do not describe exactly the same level of service.

What grease trap emptying means
Emptying removes the retained contents of the trap: wastewater, fats, oils, grease and settled food solids. For a regularly maintained system, this is often the central part of routine service.
Its purpose is to restore usable capacity before retained material occupies too much of the unit.
What a fuller cleaning service adds
After pump-out, accessible internal surfaces may still carry residue. Where the trap has been neglected, has persistent odour or shows heavier internal build-up, additional cleaning may be appropriate.
The exact scope depends on the trap design and its condition, so it is better to describe the symptoms than assume a particular procedure.

When emptying may be enough
If the trap is serviced regularly, there are no recurring symptoms and the unit is in reasonable condition, routine emptying may be the appropriate requirement. Service history helps show whether the trap normally accumulates heavy residue between visits.
When to discuss a fuller clean
Long gaps between services, hardened material, odour returning quickly, visible deposits or repeated drainage complaints can justify a more thorough assessment.
Those symptoms can also point to problems elsewhere in the drainage system, so a full clean should not be treated as a guaranteed cure for every issue.
How to request the right service
Tell the contractor when the trap was last serviced, what symptoms are present, where it is located and whether access is straightforward. Photos can help explain the condition.