Pre-qualified means that there has been some form of communication with a loan officer regarding your job, income, and types of car payments, etc.  In addition, pre-qualified status applies if your new house payment falls below a specific percentage of gross income and total debts (e.g. car, student loans, house, etc.) also happen to fall below a percentage of gross monthly income.  In the past, loan companies would then issue you a letter stating your status as being pre-qualified, meaning that you can afford your house payments.  This is helpful when you want to figure out if a lender thinks you can afford a certain amount of debt.  When you're in the process of buying a house, though, being pre-approved matters more.

Pre-approved means that the information that you have supplied has been verified.  When you have a credit report run, it checks whether or not your credit is able to meet the expectations/demands of a particular loan.  The income you told to the loan officer will be verified by a third party.  This is done by reviewing paycheck stubs or a fairly recent W-2.  In addition, the process of verifying your down payment and funds used for closing cost are reviewed by investment and/or bank statements that show whether or not the required funds are available for use.  Basically, a pre-approved status is a verified pre-qualification.  

Bankapedia's Take 

The actual pre-approval process checks to see that you are able and willing to repay a mortgage, so that verifying income and assets for closing on a house, in addition to reviewing your credit report, are the processes you will undergo.  Essentially, this is a "verify first, approve last" process.