The signing of the Declaration took place on July 4 and that is what we celebrate, but the vote was taken on July 2.
Letter from John Adams to Abigail Adams: Philadelphia July 3d. 1776
[quote]The Second Day of July 1776, will be the most memorable Epocha, in the History of America. I am apt to believe that it will be celebrated, by succeeding Generations, as the great anniversary Festival. It ought to be commemorated, as the Day of Deliverance by solemn Acts of Devotion to God Almighty. It ought to be solemnized with Pomp and Parade, with Shews, Games, Sports, Guns, Bells, Bonfires and Illuminations from one End of this Continent to the other from this Time forward forever more.