> For example, what they call a lime in a lot of countries (for example Calamansi) would be called a tiny orange in North America (we don't have that fruit here).
Calamansi limes are grown in California and usually called Calamondin limes. They're typically anywhere from orange to yellow/green when grown here.
> What we call a lime they wouldn't recognize, but if they saw/tasted it they might think it's a green lemon or something.
What country doesn't have what we call a lime? The Key lime, like the Calamansi is is native to the Philippines and available everywhere the Calamansi is. Persian limes are exported nearly everywhere.
Lots of languages don't differentiate between lemons and limes though.
A Key Lime is only vaguely a lime (they call it a Dayap and I don't think they would consider it a lime at all), that's why we call them 'Key Lime' instead of just lime. I'm putting a fine point on it, but I think when we say 'Lime' we mean something like a Persian Lime. You don't make Persian Lime pie!
As far as I know in the Philippines they don't have a common word to describe a Persian lime, and I never saw one in a store there.
Persian limes are just a cross between key limes and lemons. Before Persian limes were popularized in the 20th century, key limes were just called "limes" in the US (and still are in cocktail recipes and latin markets).