The SC CWP qualifies you for the Arizona non-resident permit. You just have to send in the Arizona non-resident permit application after you receive your SC CWP. You can request a non-resident permit application here: Arizona CWP

At this point in time the Arizona permit only gives you 1 more state: Delaware

If you'll notice in the maps below that the other states "open" to Arizona that aren't open to SC are only open to Arizona residents, not non-residents. So, unless you need the permit in Delaware there's no real reason to get the Arizona permit. If you need Delaware, please don't pay extra for a class to get the permit, the SC CWP qualifies you for it automatically, you just have to request the application and send it in. If you'll also notice that the Utah non-residence permit only open's you up to Washington State and Delaware. 

See and compare maps below.