Britain and france had already been at war in North America for 2 years when Britain formed an alliance with Prussia and france allied with Austria and Russia. At which point Prussia invaded Saxony and kicked off the seven years war in Europe and that dragged france and the uk (and their preexisting war) into it.

The two conflicts (the anglo-french war which started in north America and the Prussia vs everyone war which started in Europe) were combined into one conflict due to alliances.

The obvious comparison is ww2 which is viewed as one conflict even though the Germany vs uk and france war started two years earlier than the japan vs usa war. Did the pacific war begin at pearl harbor or at the invasion of Poland?