What is the approx. difference between the longest and shortest days of the year in Chicago, IL

Zero minutes because all days are 24 hours.

However, if you mean the day with the longest period of daylight and the day with the shortest period of daylight, the difference is (sunrise to sunset) 6 hours and 33 minutes.
December 21: 8 hours 40 minutes
June 21: 15 hours 13 minutes.

All days are exactly 24 hours long, so there is no difference.

I think you want the number of daylight hours?

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