go to smith & wesson website to see all the M&Ps. They are not in order but you will begin the see the 9mm variations.
Wiki smith&wesson and M&P and they have a great side by side matrix at the bottom to compare LxWxH.
I just went thru the same thing, trying to figure what to conceal carry.
Wiki says the shield is .200 narrower and the
9c is .5 shorter (butt) and and 1/2 inch longer.
9c also carries 5 more and that explains the width difference single vs. double stack.
good luck in your quest. mine shows up tomorrow
)