Does an iphone 4 case fit on a iphone 4s?

Well does it

Yes. Both phones were manufactured with the same form-factor.

It does fit but the position of the mute slider is somewhat changed
about <1cm so you'll maybe have to use you xacto knife to enlarge the hole.

It would but there's something to note. There were 2 versions of the iPhone 4, a GSM model & a CDMA one. Difference between the 2, no SIM slot (CDMA doesn't use SIMs), & the slight repositioning of the headphone port, volume buttons & silent switch.

The iPhone 4S essentially used the CDMA design of the iPhone 4, so if you are looking for cases that could work between the 2 it would have to be for the CDMA iPhone 4.

Yes!