The name for the observance on September 11 is Patriot Day, a national day of remembrance. This is a separate and distinct event from Patriots' Day, a state holiday observed in April. The similarity in their names is a common source of confusion.
Patriot Day, officially known as Patriot Day and National Day of Service and Remembrance, is observed annually on September 11. It was established by presidential proclamation to commemorate the nearly 3,000 individuals killed in the terrorist attacks on September 11, 2001. On this day, the American flag is flown at half-staff, and a moment of silence is observed to correspond with the times the attacks occurred. In contrast, Patriots' Day is a state holiday in Massachusetts, Maine, and Wisconsin that commemorates the Battles of Lexington and Concord, which were the first armed conflicts of the American Revolutionary War on April 19, 1775. It is celebrated on the third Monday in April and is well-known for being the date of the Boston Marathon.
In summary, while "Patriot Day" is directly associated with the date of September 11, "Patriots' Day" is not. The former is a national observance of solemn remembrance for a 21st-century event, while the latter is a regional celebration of an 18th-century historical event. The key distinction lies in the name (singular "Patriot" vs. plural possessive "Patriots'") and the completely different historical events and dates they commemorate.