I will let Jesus distinguish it.
Matt. 7:
22 Many will say to me in that day, Lord, Lord, have we not prophesied in thy name? and in thy name have cast out devils? and in thy name done many wonderful works?
These people believed in Jesus, you can't say they didn't. They taught in His Name, they gave Him the credit for all their wonderful works. They got people off drugs and crime all in the Name of Jesus.
So these people believed in Jesus.
23 And then will I profess unto them,
I never knew you: depart from me,
ye that work iniquity.
They had belief, but not trust/Faith. And their "WORKS" of disobedience to God exposed this truth.("Work iniquity") Abraham showed not only that he believed in God, but his belief was backed up with honor and obedience which proved he not only believed, like the demons, but He also trusted enough to follow God's Instructions.
This is called Faith.
The mainstream preachers of Christ's time created their own instruction and transgressed God's instructions.
Abraham did not do that.
The Mainstream preachers of Christ's time created images of God after the likeness of man in direct disobedience to God.
Abraham did not do that.
The Mainstream preachers of Christ's time refused to submit unto the Righteousness of God, and they created their own righteousness, their own definition of Holy and Unholy, clean and unclean, their own high days and traditions.
Abraham did not do that.
Jesus rejected these self proclaimed "believers" because of their "Works" of disobedience.
Jesus rejected the mainstream preachers of His time for their "Works" of disobedience.
God accepted Abraham b
ecause of his "Works" of obedience.
Gen. 26:
5 Because that Abraham obeyed my voice, and kept my charge, my commandments, my statutes, and my laws.
So these truths answer the question.
If a man claims to believe in Jesus, but creates images of God in the likeness of man, or creates their own high days, or refuse to submit to the righteousness of the God of Abraham, or is a murderer, or a thief. Then they have not the faith of Abraham.
If they don't have the Faith of Abraham, then they are not heirs to the Promise.
So once again, a man's "Works" which he will be judged by, show both himself, and those around him, his Faith.
Therefore His Holy Word's "You shall know them by their fruits".