The home inspection is where you hire a company to walk through the house and check the crawl space, attic and they will likely spend 2-3 hours at the home making sure all is safe, secure and in working order. They will note if items need attention such as repairs to a gas water heater or leaky dishwasher. Sometimes there are very few items noted such as a vent needing to be replaced or the furnace filter is in backwards. Sometimes there are major repairs the inspector uncovers. This inspection is optional, but recommended. I don't need to see the inspection report., it is for your information and protection.
The home appraisal is what the lender requires. The appraiser is the only 3rd party involved that gets to be the eyes for the lender. The appraiser will walk through the home and take pictures, measure rooms as needed and be in and out within 10-15 minutes. They will go back to their office, pull comparable home sales that have recently closed in your neighborhood and surrounding areas. Comparing age, condition, lot size, square footage of the home to similar homes, they will be able to determine a value of the home. You pay for this evaluation and the underwriter will review to make sure all meets the standards of the loan program. The appraisal also protects you from paying too much for a house.