July 4 isn't actually Independence Day. July 2 is.
The Continental Congress voted to declare independence on July 2, 1776. John Adams wrote home to his wife Abigail that July 2 would "be celebrated by succeeding generations as the great anniversary festival," with "pomp and parade," "bonfires and illuminations," from one end of the continent to the other.
Party and celebration? Yes. Correct date? No.
The official adoption of the Declaration of Independence text happened two days later, on July 4. That's the date printed on the document. That's the date everyone remembered. Adams, stubborn to the end, reportedly refused to attend July 4 celebrations because he thought they were celebrating the wrong day.
Tell that to someone grilling hot dogs this summer, and get ready for fireworks of a different type.