The French and Indian War began over the specific issue of whether the upper Ohio River valley was a part of the British Empire, and therefore open for trade and settlement by Virginians and Pennsylvanians, or part of the French Empire.
The Seven Year's War pitted the alliance of Britain, Prussia, and Hanover against the alliance of France. Austria, Sweden, Saxony, Russia, and soon enough Spain. The war was driven by the trading and imperial rivalry between Britain and France.
General Montcalm (French) leads raids deep into the American colonies, capturing Fort William Henry, and threatening to drive onto New York. British were kept at bay by Montcalm and his men and his aborigional allies.
The British capture Montreal ending the conflict in North America.