Govern, Rule are comparable when they mean to exercise power or authority in controlling or directing another or others, often specifically those persons who comprise a state or nation.
Govern may imply power, whether despotic or constitutional, or authority, whether assumed by force, acquired by inheritance or through election, or granted by due processes of law, but it usually connotes as its end the keeping of the one or ones directed or controlled in a straight course or in smooth operation, where perils are avoided and the good of the individual or of the whole is achieved.
Rule is not always clearly distinguished from govern. Often it implies the power to lay down laws which shall determine the action of others or to issue commands which must be obeyed; it therefore commonly suggests the exercise of arbitrary power and is not ordinarily used of one that exercises authority over the people as an elected official.