The original independence resolution was passed on 7/1 with nine in favor, two against, one delegation split, and one abstention.
On 7/2 the vote was taken again. This time it was "unanimous" (with one abstention).
The Declaration was "adopted" on the 4th. I've never been completely sure what that means. I don't know if they took a vote on it or just finished critiquing it so that there were no further objections. Only John Hancock and Charles Thomson signed that day.
On 8/2 fifty members of the Congress signed the freshly drafted parchment with the final wording. This is the "signing" most people think of.
From what I’ve read, it seems that the vote on the 4th was likely on the final wording of the document.
Oh, for a time machine to go back and watch!
But the signatures continued to be added after August 2, 1776.
My wife is descended from Thomas McKean, one of the "Signers" of the Declaration of Independence. A number of her aunts and (now-deceased) great-aunts are or were particularly proud of that.
I'd just nod and smile . . . knowing that McKean didn't sign the Declaration of Independence until 1781.