https://en.wikipedia.org/wiki/Continent points out how they "are generally identified by convention rather than any strict criteria" and lists "several ways of distinguishing the continents", with the 7-continent model, two different 6-continent models. It also mentions the "four-continent model consisting of Afro-Eurasia, America, Antarctica, and Australia", as well as how there were only three discrete landmasses present during the Pleistocene ice ages, when the Bering Strait was instead land.
You can see the cultural influence in:
> In the English-speaking countries, geographers often use the term Oceania to denote a geographical region which includes most of the island countries and territories in the Pacific Ocean, as well as the continent of Australia.
> In some non-English-speaking countries, such as China, Poland, and Russia, Oceania is considered a proper continent because their equivalent word for "continent" has a rather different meaning which can be interpreted as "a major division of land including islands" (leaning towards a region) rather than "land associated with a large landmass" (leaning towards a landmass).
They are not defined by geology nor continental plates. For one, the word and current use is far older than our first glimmers of understanding plate tectonics. https://www.etymonline.com/word/continent says the meaning in the 1550s was "continuous tract of land" and by the 1610s became "one of the large land masses of the globe".
FWIW, the North American plate includes some of the continent of Asia. https://en.wikipedia.org/wiki/North_American_Plate