Is the longest day of the year the same length all over the world?

Well, the length of every day is 24 hours all over the world.
You must be talking about the length of daylight.

On the equator, the longest daylight (sun up in the sky) is just about
12 hours, twice a year, around March 21 and September 21.

At the north and south poles, the sun is up in the sky for SIX MONTHS.