The Declaration of Independence and the Constitution are two very separate yet intinsically linked documents. Formally, the Declaration has no legal power whatsover in the United States, while the Constitution is the foundation of all legal power in the United States.
Even the tone of the documents have clear differences. The Declaration is far shorter and is a passionate document, using high language to describe the rights of man and how King George III of England had violated these rights. The Declaration is an ideological and philosophical document containing what the signatories felt the powers of government should be. It contained strong religious and spiritual symbolism, though not necessarily pertaining to any one faith.
The Constitution is a much "drier" document, outlining in plain English (from a legal standpoint) what the setup and powers of the government were. In keeping with the ideals added by the Bill of Rights, all religious references were removed from the Constituion (compare to the famous beginning of the Declaration, "...that all men are created equal, and endowed by their Creator with certain unalienable rights...")
Hope this clears it up for you.
