Maybe Think of American options like concert tickets that you can use anytime before the show. Unlike tickets that only work on the day of the event (like European options), these tickets (American options) can be used whenever you want. Figuring out their price is tricky because you need to consider when it's best to use them, making it harder to have a simple formula like we do for tickets with fixed dates.
Sorry, did you mean to reply to a different comment? This doesn't appear related to what I was discussing (the etymology of the terms; I'm aware of what they mean).
