America is the only country that celebrates the Fourth of July. Many other countries celebrate an independence day (in the Bahamas, it is July 10th, I believe) but to my knowledge no other country's independence day coincides with ours.
Independence Day July 4, 1776, was the day America declared its independence from the British. On July 4th two founding fathers signed the Declaration of Independence, days and weeks later it was signed by the rest. The Fourth of July is celebrated by Americans as Independence Day.
Do people in the United States celebrate United States Day? "Independence Day" is not solely associated with just American independence (July 4th). Mexico has an Independence day (May 5th), Greece has an Independence Day (March 25th). Malaysia's is August 31st.
The Netherlands don't realy have a day when they celebrate their independence like for example America, since it has never been a colony or something. But they do have a day when they celebrate that the Netherlands were freed from the Germans in the Second World War: the fifth of May.