Is a compartmentation survey a fire risk assessment?

Not quite. They are separate jobs and you may need both.

A fire risk assessment covers the whole building. The assessor checks the alarm, the escape routes, the signs and how the building is run. They look at the walls too, but they cannot get above every ceiling or into every cupboard, so the report may say compartmentation could not be checked.

A compartmentation survey picks that up. It covers the walls, the floors and the holes where pipes and cables go through them. It does not cover the alarm or the escape routes.

So if your risk assessment says compartmentation could not be checked, a survey is what fills the gap. Give the report to your assessor afterwards and they can update theirs.

A fire door inspection is different again. It covers the doors and nothing else.