The PC CGA spec only allowed for 16 colors due to the palletizing it used. Further, only certain colors were possible since the output wasn't actually analog. The outputs were rather generated directly off the outputs of 74 series logic with a couple resistor dividers (some didn't evne have that, only allowing 8 colors), and that's why CGA video signals are conventionally "larger" voltage-wise than modern analog (VGA and friends) signals.
CGA monitors had analog input paths and will accept anything at the correct resolution/timing. It's possible to display any number of colors on a CGA monitor, but the PC wasn't capable of generating more than a few at the time. Arcades didn't have this limitation, of course.
Your 16 number also sounds wrong (too high). I rember getting 4 on the screen at once, and a choice of 8. EGA offered a choice of 16 at once from a larger pallete, IIRC. Cyan, Magenta, White, and Black seemed to be the most common choice, for some ugly reason.