This can be rather confusing...
Unfortunately, there is no real distinction in Persian...دولت is used for both.
With regard to the U.S. system, we have only one government, which started with George Washington in 1789. The period of a time which a president serves is called his "administration".
Since Washington's time we have had 44 "presidencies", but only 43 men have served. Grover Cleveland was the 22nd and 24th president, and is counted twice as president.
See
http://en.wikipedia.org/wiki/List_of_Presidents_of_the_Unite...If we use دولت چهل و سوم به ریاست جمهوری بوش
it sounds like we count governments, which is not the case.
دولت چهل و سومین رئیس جمهور آمریکا، بوش
makes it more clear that we are talking about the time that Bush, the 43rd president, was president.