I think you got it backwards.
In English, the letter S is often pronounced like a Z. Examples:
is, his, hers, music, phase, phrase, hose, pause, plays.
The standard S sound (what 5-year olds learn in kindergarten) is the sound similar to C followed by E, I, or Y. Examples:
sand, scoff, send, sign, skunk, sleep, small, snore, sore, spark, spherical, square, massive, stellar, sun, swap, symphony.
The letter C (according to my 5-year old) sounds ka-ka-ka. Examples:
cable, back, club, acme, acne, consider, acquire, cross, cup.
But followed by certain vowels, C will sound like an S. Examples:
cenacle, acid, cynical.
This is not counting such delightful oddities as Sean, mission, ancient, asthma. And let us leave CH and SH alone for now.
It is all so deliciously confusing, not as tidy as German or Romanian. Good luck.