Lime is the English name of calamansi.
Other English common names of calamansi include, Philippine lime, calamonding, calamondin orange, calamandarin, golden lime, Panama orange (also used for kumquats), musk orange, bitter-sweets and acid orange.
So if you've eaten a Lime then really you've eaten Calamansi.
I've always just called them Limes as it's easier to spell it and easier to say the name Lime than it is to say or spell Calamansi.
But if you're looking for Calamansi in the USA most people would know them as Limes.