The purpose of the Declaration of Independence is to explain to foreign nations and King George III why the colonies had chosen to separate themselves from Great Britain and become independent.
A presidential inauguration is a ceremonial event centered on the formal transition of a new president into office, its important it’s seen as a celebration because it shows the start of a new president.
It established the principle that everyone is subject to the law. Even the king. It also guaranteed the rights of individuals, and the right to a fair trial.