The Declaration of Independence states that the United States of America is a country that should be recognized as an independent country that is free from England. This actually contains a lot of things about the king of England that will ensure that the United States will not be under England anymore.
The constitution, on the other hand, is going to be different. It will have the different laws of the land that will make sure that people will stay disciplined, and they will do things according to the constitution.
The aim of the constitution is to make sure that people will follow the rules and regulations, depending on what is considered to be right.