How are the declaration of independence and the declaration of the rights of man and citizen different?

One way in which they are different:

The Declaration of Independence speaks of a Divine Creator and The Declaration of the Rights of Man speaks of a Supreme Being.

The Declaration of Independence (1776) famously asserted, "We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness."  America's founding fathers tended to speak in religious terms associated with the Christian tradition, even though a number of them were more like Deists in their own beliefs.  Deists believe that there is a God who created the world, but set it up to run by natural laws and did not intervene in a personal way in its operation.The Declaration of the Rights of Man and Citizen (1789) was less overt in ascribing the rights of human beings to God as Creator.  That declaration of the French Revolution stated, "The National Assembly recognizes and proclaims, in the presence and under the auspices of the Supreme Being, the following rights of man and of the citizen."  They were taking using more overtly Deist language, acknowledging a Supreme Being that was the reasonable force governing all things, but seeing human beings in society granting rights according to the actions of a just government.