Q: My contacts won't import from a galaxy s4 SIM card onto an iPhone 4s

No, well of course it will not work, because no iPhone ever stores any data on a sim card - you need to get the contacts onto your computer and then sync with your iPhone that way and then search the app store for an app to help you do this, because it is not possible to transfer straight from a sim card directly in this way.

No, this is not the case - anything like that needs to be downloaded to your computer first and syced via iTunes or some other way, so you need to do a search of apps to help you achieve this, but the iPhone cannot import directly from a sim card in this way.

the iPhone cannot import directly from a sim card in this way.

100% WRONG! See: http://support.apple.com/kb/HT4994

Not sure why that wouldn't be working for you. Have you verified that the contacts did copy to the SIM successfully from the Galaxy?