“…without faith it is impossible to please him: for he that cometh to God must believe that he is, and that he is a rewarder of them that diligently seek him.” (Hebrews 11 KJV)
The way I see it, Faith and belief are very closely related.
Example: You BELIEVE an elevator will bring you safely down to main floor..so you walk in WITH FAITH that it will.
See? We use faith everyday. Regarding Salvation it is the belief in the object of our faith that makes the difference.
A believer..believes the atonement for sins through the only begotten Son of God on the cross. Now believing on Christ alone for their justification and forgiveness of sins, they are saved.
Then they act on that truth in life by faith. Belief saves..not just faith. Faith must have an object to believe on… that object is Jesus Christ to be saved.
That is how I see it.