All believers are muslims, but not all muslims are necessarily believers!

 

Verses 14-15 of Chapter 49:

The bedouins say: "We believe.'' Say: "You do not believe. But say, `We have submitted,' for Faith has not yet entered your hearts. But if you obey Allah and His Messenger, He will not decrease anything in reward for your deeds. Verily, Allah is Forgiving, Most Merciful.'' Only those are the believers who have believed in Allah and His Messenger, and afterward doubt not but strive with their wealth and their lives for the cause of Allah. Those! They are the truthful.