There were, as you say, four wars that were fought between France and Britain for control of North America. In the British colonies of North America, these wars were called King William’s War (1689 to 1697), Queen Anne’s War (1702 to 1713), King George’s War (1744 to 1748) and the French and Indian War (1754 to 1763).
The most important thing to know about all of these wars is that they were not primarily wars about North America. Instead, North America was but one theater in much larger wars. The four wars mentioned above were called the following by people in Europe: War of the League of Augsburg, War of Spanish Succession, War of Austrian Succession, and Seven Years’ War. All of these wars can be seen as world wars. They came about because of events in Europe, not because of events in the colonies in North America. For example, the War of Spanish Succession was fought because England, Holland, Austria, and Germany did not want the Bourbons (a dynasty that was ruling France) to also take over the Spanish throne after Charles II of Spain died. The fighting in North America only came about because that was a place where the two sides could try to hurt one another.
Thus, the wars for domination of North America were parts of larger wars that were caused by rivalries in Europe.