Vines expository Greek dictionary.:
The main elements in Faith, in it's relation to the invisible God, as distinct from Faith in man, are especially brought out in the use of the this noun and corresponding verb, "pisteuo". They are 1) a firm conviction, producing a full acknowledgement of God's revelation of truth. 2). A personal surrender to Him 3) a life inspired by such surrender. Prominence is given to one or the other of these elements according to the context. All this stands in contrast to BELIEF in its purely natural exercise, which consists of an opinion held in good faith without the necessary reference to it's proof. The object of Abraham's Faith was not God's promise ( that was the occasion of the excersise) His Faith rested on God Himself. Rom. 4:17,20,21
This is the exact definition of pisteuo out of the Vines Greek dictionary, word for word with nothing left out. The only time "Belief" is mentioned is when they give the same disclaimer that the Strong's gives, pisteuo means NOT just to believe