The "belief" issue is almost entirely exclusive to advanced Protestantism (those after Luther) and more especially to movements from the Second Great Awakening. The type of "belief" that schnell admits is a "loose" usage is indeed that.
Movements from the American Great Awakening eras redefined theological concepts, mostly from a lack in formal and classical education. Groups like the Mormons and Jehovah's Witnesses share an almost identical understanding of "belief," and mistakenly apply this concept to the Great Christian Churches.
In Catholicism, Orthodoxy, Judaism, and most Protestant churches mere belief is considered unsatisfactory. In Christianity, for instance, James tells Christians that to have faith in God is to do no better than the demons. (James 2:19) Groups like the Mormons and JWs, however mix the terms "faith" and "belief" up so much, that even some ex-adherents of both movements almost never untangle the concepts well enough to understand the vast differences involved. This may explain the high percentage of atheism among existing born-ins from both movements in comparison to those converts who come from other religious groups (existing converts from other faiths generally do not become atheists).
Whereas JWs and Mormons are constantly having to tell people they do indeed "believe" in Jesus, rarely do they explain they have "faith" in Jesus. JWs also make the mistake of accepting Hebrews 11:1 as a definition of faith, whereas the text is merely speaking of various facets of the concept in relation to the material that follows in that chapter.
The words used in both Scripture and doctrinal treatise in the classical religions define "belief" as a mental grasping and assent to a concept, something that is static. "Faith" refers to something neither static nor limited to the mind. The word means to demonstrate one's trust.
To believe in someone, in the Judeo-Christian manner, means to attribute something to the subject either based on past evidence or merely credit. But to have faith in someone is to do what they ask of you, to literally act when the subject of faith is absent. The expression "faith can move mountains" is actually a mistranslation. The Greek word Jesus used means "faithfulness"
The difference is enormous. If one believes God will move a mountain, the person will pray and then sit on the side of the road waiting for God to act. This is not faith, just belief. Faith, on the other hand, or better faithfulness will cause a person not merely to pray but to then begin pushing the mountain on their own. A faithful person does wait on God to move the mountain. A faithful person instead expects God to bless their own efforts of mountain-moving.