The history of The Netherlands is quite complicated, perhaps messy is a better word.
In the Treaty of Verdun (France, 843) the Empire of Charlemagne (742-Aachen 814) was divided into three parts, each part ruled by one of his grandchildren, sons of Louis I (778-840). The Low Countries became part of the middle part, which stretched out from Friesland (now a province in the north of the Netherlands, and roughly between Reims/Verdun/the Rhone/Avignon in the west and the Rhine/Elzas/Venice/Rome in the east. This part was ruled by Lothar I (795-855) and was thereafter known as Lotharingen/ Lorraine. The western part, from the north of France to the Pyrenees, was ruled by Charles the Bold (823-877). The eastern part, from the Rhine to Vienna, Austria was ruled by Louis II (806-876). The Low Countries was a collection of some 17 counties. Some had a Duke (Brabant and Limburg), others had Counts (Holland, Flanders, Hainault/Henegouwen), and others were run by Bishops (Utrecht, for one).
Fairly soon the Low Countries became officially part of the Germanic part ruled by the Emperors. However, the people of the Low Countries disliked interferences from lands so distant and regarded themselves as fairly independent. So they had to repulse a few imperial armies.
The County of Holland at one stage stretched from Flanders to Bremen in Germany; it encompassed the modern provinces of Zeeland, Zuid-Holland, Noord-Holland, Friesland and Groningen. There are several explanations to the word 'Holland'; one is 'Holtland' land where wood (hout) was found. Another explanation is 'Hol' means hollow, low.
When Philip II of Spain (1556-1598) repressed the Protestants and wanted to extract huge taxes to pay for wars he was waging elsewhere, the Low Countries revolted (1568). But, on Januari 23, 1579, with the Union (Treaty) of Utrecht the seven northerly counties/provinces united against Spain, and by the Union of Atrecht (= Arras, France), on Januari 6, 1579, the 10 southerly remained with Spain under the leadership of the Duke of Parma. This division created the differences between the Dutch and the Belgians. The north was Protestant and the south remained Catholic.
The "Republiek der Verenigde Nederlanden" (Republic of the United Netherlands), as it was thereafter called, united seven counties/provinces: Zeeland, Holland, Utrecht, Gelderland, Drente, Groningen and Friesland. Each county/province had their own government, but they appointed a military 'stadhouder' and several counties elected the same. As a result in Holland (and a few others counties) elected Maurits, Frederik Hendrik, Willem II and Willem III, the latter also king of England (1688). In Friesland (and a few other counties) selected the branch of the Counts and Princes of Nassau-Dietz as their "stadhouder." As Willem III (1672-1702) died without children, in the low countries he made the Prince of Nassau Dietz (Johan Willem Friso) his heir and from then on his family became the House of Orange and Nassau.
Holland, perhaps I should say Amsterdam, became one of the most powerful states in Europe and they employed mercenary soldiers from Germany to wage their wars. In the 17th and 18th century Holland fought four sea-wars with England, in order to protect their overseas trade and colonial expansion. In the second war (1665-1667) they landed in England and went up the Thames as far as Chatham. And as the soldiers employed by Holland came from the German city of Dietz, in England the cry went up 'the Dietz are coming, the Dutch are coming'. As a result we are called Dutch after a town in Germany. The fourth war (1780-1784) was caused, due to Amsterdam supporting the American rebels by selling arms, England declared war again in 1780 against Holland.
On November 30, 1813, after the liberation from Napoleon, the son of stadhouder Willem V returned from England, and landed in the fishing village of Scheveningen, near The Hague. On March 16, 1815 he became the first king, Willem I of the new kingdom of the Netherlands. On October 7, 1840 he abdicated in favour of his son Willem II, and moved to Berlin where he remarried.
Noord- en Zuid-Holland were, and still are, by far the richest, the most populated, and most politically powerful provinces of the Netherlands, which is one of the reasons, I presume, why foreigners confuse Holland with the Netherlands as a whole.
To call the Netherlands "Holland" is as incorrect as calling the USA "New York" or a Scotchman/Welshman an Englishman.