Assurance: A certainty or confidence of mind or matter.

Hope is the seed of the Assurances. Hope is desire and possibility, as a seed it takes root as Belief. Believing, the active form of Belief, becomes the stalk which branches into Faith which is a spiritual concept. Faith then blossoms as Trust, its active form. This plant is both the parent and the offspring of the Unconditionals: Grace, Agapé and Forgiveness, for the Unconditionals yield assurance which in turn yields the Unconditionals; together they are Self-replicating.

Often these words are used interchangeably. They seem to have begun as a single word; in the Greek text of the New Testament the word pistis (n. pistis, v. pisteuein) is translated into English as either Trust, Faith, Believe or Belief. When defining words it is important to look both at their present and historical usage.

Merriam-Webster Online Definitions Faith
(bold headings are my own)

Faith as Promise

• allegiance to duty or a person: loyalty
• fidelity to one's promises
• sincerity of intentions

Faith as Trust

• belief and trust in and loyalty to God
• belief in the traditional doctrines of a religion
• firm belief in something for which there is no proof
• complete trust