This is a common question when purchasing a home the first time, or in many cases by many that simply did not want to look ignorant of the process and did not ask. I would always recommend you ask all questions on items you do not understand, as the home buying process can be confusing, and it has many moving parts. A professional will gladly explain the process to your comfort level, or you should consider getting a new agent or mortgage loan officer.
The home inspection is optional and usually ordered to protect the buyer from purchasing a home with issues not known or disclosed by the seller. It is done by a 3rd party licensed home inspector. Their job is to inspect the property on behalf of the individual purchasing the inspection to find any issues with the home such as foundation issues, roof damage, plumbing, electrical problems, or sometimes just small irrelevant items such as a crack in the drywall, which will just about occur on every home after the foundation moves a bit. The crack on the drywall can be a sign of foundation issues, but most of the time is nothing to worry about. Some spackle and paint will usually handle the issue, but do not be surprised if more come about over the changes in season as the earth hardens in winter or softens with rain. It is a natural occurrence, but one that must be watched accordingly.
The appraisal of the home is done to inspect the home for obvious issues to the eye and not as thorough of a home inspection to protect the home buyer. It is primarily ordered to protect the lender. The appraisal is ordered to determine the value of the property. The value will be compared with the purchase price to make sure you are not paying too much for the home, and the lender is not lending more than the home is worth. The value used for your loan will be the lower of the two numbers.
For Example: If the purchase price is $200,000
The Appraised value is $190,000
The lender would then use the value of $190,000 to lend on. If the loan requires 20% down for example, then the buyer would have to put 20% down of the $190,000 of $38,000, but since your purchased for $200,000 you would need to also bring the difference of $10,000 to meet your obligation of the contract for a total of $48,000, or you would have to discuss with your agent to negotiate a lower price due to the lower value and decide if you would still like to purchase the home. In some booming markets, the price over value is common and the buyer will have to pay the difference, but in most cased the agents can negotiate the price down to value or close to it to keep the contract in place and not re-list the property. If the value comes in higher than the purchase price, the lender will use the purchase price as value, and you just made a great investment and already have equity built in your new home.
We hope this helped explain the inspection and appraisal process and the difference between the two. Good luck and good house hunting!