I assume you are talking about saving contacts? These are two different options. The sim card is provided by your carrier and put into your phone. It's what activates your service. It can be transferred between different devices for example if you got a new phone, to activate your new device.
If your contacts are stored on the sim, they would go with the card into any device, meaning you would have your contacts immediately in your new device.
If they are stored on the phone, they will remain on the phone as you switch devices. Though, you can pretty easily back up/sync your contacts through your Google account or through apps off the play store.