In our area of Northern California, the selection, costs, and order of inspections is negotiated in the purchase contract.  Customarily the seller pays for the wood destroying pest inspection and the buyer pays for a whole house inspection, but I have seen this flip-flopped many times.  One myth about inspections is that the property must “pass” inspection.   Not so.  These inspections are advisory.  When issues appear, the buyer has the right to request repairs.  The seller can take action, or not, and the buyer can withdraw from the transaction without penalty as long as the agreed-upon inspection period has been observed.   Here is the usual list of inspections involved in our residential transactions:

Wood Destroying Pest

Whole House

Heating and Air

Chimney

Parcel Corners

Roof

Well

Septic or Sewer

If the whole house inspector flags some component (electrical, plumbing, structural, etc) of the property, that finding may initiate another inspection.