Govt. is only a written short form of government. You will see it on signs, in newspapers, in tight headlines, and in notes where someone is saving space: Govt. offices, the govt. plan. It is not a different word and it does not change the meaning. Though actually, you should not say it aloud as “govt.” When you read it, you say government. It is a little old-fashioned and a little official on the page; many writers now just write government in full, or use the even shorter gov in very informal messages. It is not the same short form as Gov., which often means Governor — a person, not the whole system.