Importing SIM card contacts

The ability of a phone that saves to the SIM will make a big difference. Of course, as you have found, it can make a difference with the iPhone, and at times can make a difference with other devices too, due to the way they are saved. Most SIM cards cannot save good information and it isn't formatted correctly to be read. Once the contacts are in the iPhone they can be saved, imported and exported in several ways that most phones can read.

There is no data stored on the sim card.

Contacts are synced to whatever cloud or mail program you use.

Are you just now moving to an iPhone from the other phone? If you have been working with an iPhone and are looking for contacts, then razmee209 is correct, the iPhone does not write contacts to the SIM. However, if you were coming from another device to the iPhone, you can import those SIM contacts, but they are going to be subject to the way the other phone formatted them and the transfer to the iPhone. It is not necessarily a clean import, it is going to depend on what the other device was.