Both the lime and calamansi are limes so yes they are in some ways the same thing.
The Calamansi is basically a Philippine lime.
Calamansi Lime is a cross between a citrus and a Kumquat.
So they are almost the same thing but actually lime and calamansi are somewhat different.
The lime and calamansi seem to have a different taste at least in my opinion when I've tried them both.
The Calamansi in my opinion has a better and less sour taste to it than Lime does but your tastes can vary.
What one person may like somebody else may not.