There is difference in the reputation on Stack Overflow in the site header and below the profile image. Is that a bug?
No it's not a bug. The reputation number at the top of the page gets live-updates. But the reputation number under your gravatar does not.
When you loaded the page, you had 1620 rep. Then your reputation increased to 1628. The live-updates will update the number at the top, but not the number under your gravatar.