What's the difference between an administrator and an executor?
  They're both fiduciaries (someone who acts for another person, in a position of trust).
An executor is the one named in a will to be in charge of the estate.
An administrator is the person in charge of the estate of someone who died without a will.  (There is a special kind of administrator whom the court appoints even when there is a will, either becuase the will doesn't name an executor, or no one named is available to handle the job.  This is called an Administrator With the Will Annexed or Administrator WWA, or for those who use the Latin terms, Administrator Cum Testamento Annexo or Administrator CTA.)
And to get one more term out there, the person who died is called the decedent.
Both an administrator and an executor are subject to the jurisdiction of the Probate Court, and have similar duties.  They gather the assets of the estate, file the tax returns for the estate and for the person who died, determine and pay the creditors, and distribute the assets to the beneficiaries (if there is a will) or the heirs (if there is no will).  An administrator's authority is only what the law provides, which can be pretty limited.  An executor (and an Administrator CTA/WWA has all of the statutory powers, plus whatever additional powers the decedent included in the will.
For example, an administrator has to post a bond, and may have to provide surety on the bond.  In Massachusetts, the bond is a simple matter, basically just filling out a Probate Court form correctly.  If the court determines that sureties are required to guarantee the administrator's proper handling of the estate assets, the administrator has a difficult choice: get a corporate surety bond (which can be expensive, and counts against the administrator's credit score which can foul up plans for getting a mortgage), get a friend or relative to act as surety, or decline to serve. 
By contrast, a will can say that an executor doesn't have to get sureties.