Belief  Vs  Faith
Belief: the truth of something offered I except as truth.
Example:  I believe when I sit in this chair, it will hold me up.

Faith: complete trust in something for which there is no proof and then acting upon it.  Firm persuasion; conviction based upon hearing.

Example:  I sit in the chair, for until I sit in the chair, I do not have faith. 

I can believe Jesus died for my sins and have everlasting life, but until I have faith in it by acting on it by trusting and excepting Jesus as Lord and Savior, it will never happen
Another way of looking at it.

Harry:   Fred, do you belief I can push this wheelbarrow over this tight rope over the Kings River?

Fred:   Sure do Harry!  I believe you can do it.

Harry:   Are you 100% possessive I can do it?

Fred:   I am 100% possessive you can push that wheelbarrow over this tight rope over the Kings River!

Harry:   Then get into the wheelbarrow!

Fred:  NO WAY!

Harry:  Then you believe but don't have faith
If you really believe he can do it, then "faith" says to get into the wheelbarrow.  If you never get into the wheelbarrow, then you don't have faith.  Faith if acting on what you belief.

Romans 10:17   So then faith cometh by hearing, and hearing by the word of God.

Heb 11:3  Through faith we understand that the worlds were framed by the word of God,

Heb 11:4 By faith Abel offered unto God a more excellent sacrifice than Cain

Heb 11:5  By faith Enoch was translated that he should not see death

Heb 11:7  By faith Noah, being warned of God of things not seen as yet, moved with fear, prepared an ark to the saving of his house;

Heb 11:8  By faith Abraham, when he was called to go out into a place which he should after receive for an inheritance, obeyed

Heb 11:11  Through faith also Sara herself received strength to conceive seed, and was delivered of a child when she was past age, because she judged him faithful who had promised.

Heb 11:6  But 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.