Well, if nothing else, it should at least be easy to check that (even if they existed elsewhere earlier) Samuelson thought he was independently inventing these terms, right? Except, in the paper where he supposedly invented these terms [3], he introduces them as follows:

> However, the simple integral (24) does give a solution under all cases to the simpler case of a warrant that can be exercised only at the end of the period T. We might call this a "European warrant" by analogy with the "European call," which, unlike the American call that is exercisable at any time from now to T, is exercisable only at a specified terminal date.

Note that nowhere previously does the paper make use of the "American" or "European" terminology, so it sounds like "European call" and "American call" here are references to pre-existing terminology -- suggesting that he didn't invent it after all! Huh.

Well, that got murkier than I expected. Don't really want to investigate further right now, but sounds like he didn't actually invent the terminology after all...?

[1] https://www.macroption.com/american-vs-european-options/

[2] https://www.youtube.com/watch?v=RbIzwTGN3Yc&t=11m

[3] https://link.springer.com/chapter/10.1007/978-3-319-22237-0_...