The short answer you’re only required to have the 203k Consultant inspection. However, it is a good idea to have both.
Let me explain; The 203k Consultant considered more experienced than Home Inspectors. This belief is not entirely true. Home Inspectors who belong to InterNACHI or ASHI receive outstanding continuing education programs. Keeping the inspectors up to date on the latest standards and materials used in home construction.
203k Consultants usually evolve from General Contracting. Some Home Inspectors under the new rules with enough experience can become 203k Consultants.
Consultants typically have a better grasp of the costs of renovation and experience with alternative options in materials and methods of construction.
The cost of a Consultant and a Home Inspector are minimal when compared to the savings you may get because of their experience and advice.
One more point. The number of trained eyes on the project lessen the likelihood of mistakes. Get the home inspection and give a copy to the Consultant being sure you have not missed anything important.