That’s typically just a home inspection.
If they want more then that they need to specify exactly what they are needing. Some may need a specific form filled out. If so there is a registration required. The detail of the inspection and the fee charged would be dependent upon what is requested. (92051 form is a 10 minute $100 inspection that takes more time to do the invoice, report, and photo pages than it does to do the inspection. A 203K has additional requirements as well. ) Some may need inspections done to “fha standards”, if so, ask them what standards they are needing (reference an fha document) and go from there.
There are “no requirement, fha inspections” that are just inspections (“I’m getting an fha loan and they say I need to have the house inspected.”).
There are “fee inspections” that are the 92051 form mentioned above.
There are “compliance inspections” that are 1004-d forms that can only be done by appraisers. (I sub these to an appraiser friend of mine.)
There are 203K inspections that can only be done by 203K consultants.
There are other fha/hud inspections that are also only done by appraisers along with their appraisal.
Bottom line here is that you haven’t given us enough details on your question for us to give you an answer.
“New Purchase Inspections for FHA” could be a half dozen different things. More details are required.