I'm late getting this posted, but for the record, today, February 22, is Washington's actual birthday.
The Washington's Birthday holiday in the United States is observed on the third Monday in February, which never actually falls on Washington's birthday. But then again, the day Washington was born wasn't the 22nd of February in the American colonies by the calendar of the time.
That's because the British Empire did not switch from the Julian to the Gregorian calendar until 1852, long after almost all of Europe had done so. (The other major hold-outs were Sweden, which followed in 1853, and Russia, which continued using the Julian calendar until 1918. That's why the Communist October Revolution took place in November 1917 as pretty much everybody else reckoned dates.)
The Julian calendar has a leap year every fourth year, which is 3/4 of a leap year too many per century, if you want the calendar to stay more or less in sync with the seasons. The Gregorian calendar avoids that problem by treating years ending in 00 (which are always leap years on the Julian calendar) as regular years unless they're divisible by 400. Hence, 1600 and 2000 were leap years in the Gregorian system, but 1700, 1800, and 1900 were not.
When adopted by the Catholic Church in 1582, the calendar also skipped ahead 10 days, which put the celebration of Easter relative to the spring equinox back in line with what had been intended by first Council of Nicea in 325. When Britain got around to converting, the discrepancy between the two calendars had increased from 10 to 11 days because 1700 was a leap year by the Julian calendar but not the Gregorian.
To complicate matters further, Britain had previously followed an old practice of treating March 25 as the start of the New Year. The Gregorian convention was and is to start the year on January 1. So Washington's birthday didn't just fall on different days of the month by the two calendars, but in different years. Washington was born 11 February 1731 O.S. ("Old Style"), but on the Gregorian calendar that was 22 February 1732 N.S. ("New Style"). That's what makes today, 2016 February 22, his birthday as we now count dates.
I'm not sure whether the date was written day-month-year at the time, as the British currently do, or month-day-year, the American convention. As for me, I've come to prefer the more rational UNESCO/ISO convention of writing year-month-day, which is consistent with giving the time in terms of hours-minutes-seconds, but I digress.
A lot of people refer to the official holiday as some variation on "Presidents Day," but the official name at the federal level is "Washington's Birthday." According to Wikipedia, it's been officially designated as "Presidents Day" by the three states of Nevada, New Jersey, and Oregon. It's also "President's Day" (apostrophe before the S) in Alaska, Idaho, Maryland, Nebraska, New Hampshire, Tennessee, West Virginia, and Wyoming, and "Presidents' Day" (apostrophe after the S) in Hawaii, New Mexico, North Dakota, Oklahoma, Puerto Rico, South Dakota, Texas, Vermont, and Washington.
But even here in North Carolina, television stations and stores insist on calling it "Presidents Day" though that's not the official state or federal name of the holiday.
Montana, Colorado, Ohio, Utah, and Minnesota refer to it as some variation on "Washington's and Lincoln's Birthday," Alabama calls it "George Washington/Thomas Jefferson Birthday," though Jefferson wasn't born in February at all but rather 1743 April 13 (which was 1743 April 2 O.S.).
Finally, in Arkansas it's George Washington's Birthday and Daisy Gatson Bates Day. Daisy Gatson Bates was a civil rights leader who helped integrate the Little Rock schools.