assurance, belief, believe, faith, fidelity

“Faith (πίστις)” From Concise Bible Dictionary:

This is a kindred word to “believe,” and indeed the two cannot be separated. In the O. T. the word “faith” occurs but twice (Deut. 32:2020And he said, I will hide my face from them, I will see what their end shall be: for they are a very froward generation, children in whom is no faith. (Deuteronomy 32:20); Hab. 2:44Behold, his soul which is lifted up is not upright in him: but the just shall live by his faith. (Habakkuk 2:4)). The words are emun, emunah; but aman is often translated “to believe.” The first time this occurs in the O. T. is when it is said of Abraham that "he believed in the Lord, and he counted it to him for righteousness" (Gen. 15:66And he believed in the Lord; and he counted it to him for righteousness. (Genesis 15:6)). This is referred to in Romans 4 where the faith of the believer is counted for righteousness, and the conclusion is drawn that if any believe on Him that raised up Jesus the Lord from the dead, righteousness will be reckoned to them.
This may be called saving faith. It is confidence in God founded of His word; it is believing in a person, as Abraham believed God. "He that believeth on the Son hath everlasting life" (John 3:3636He that believeth on the Son hath everlasting life: and he that believeth not the Son shall not see life; but the wrath of God abideth on him. (John 3:36)). There is no virtue or merit in the faith itself; but it links the soul with the infinite God. Faith is indeed the gift of God (Eph. 2:88For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: (Ephesians 2:8)). Salvation is on the principle of faith in contrast to works under the law (Rom. 10:99That if thou shalt confess with thy mouth the Lord Jesus, and shalt believe in thine heart that God hath raised him from the dead, thou shalt be saved. (Romans 10:9)). But true faith is manifested by good works. If a man says he has faith, it is reasonable to say to him, "Show me thy faith" by thy works (James 2:14-2614What doth it profit, my brethren, though a man say he hath faith, and have not works? can faith save him? 15If a brother or sister be naked, and destitute of daily food, 16And one of you say unto them, Depart in peace, be ye warmed and filled; notwithstanding ye give them not those things which are needful to the body; what doth it profit? 17Even so faith, if it hath not works, is dead, being alone. 18Yea, a man may say, Thou hast faith, and I have works: show me thy faith without thy works, and I will show thee my faith by my works. 19Thou believest that there is one God; thou doest well: the devils also believe, and tremble. 20But wilt thou know, O vain man, that faith without works is dead? 21Was not Abraham our father justified by works, when he had offered Isaac his son upon the altar? 22Seest thou how faith wrought with his works, and by works was faith made perfect? 23And the scripture was fulfilled which saith, Abraham believed God, and it was imputed unto him for righteousness: and he was called the Friend of God. 24Ye see then how that by works a man is justified, and not by faith only. 25Likewise also was not Rahab the harlot justified by works, when she had received the messengers, and had sent them out another way? 26For as the body without the spirit is dead, so faith without works is dead also. (James 2:14‑26)). Otherwise, if the faith does not manifest itself, it is described as “dead,” and is altogether different from real, active belief. A mental assent to what is stated, as a mere matter of history, is not faith. A natural man can believe such things: "the devils also believe and tremble," but true faith gives joy and peace.
There is also the power and action of faith in the Christian's walk: "we walk by faith; not by sight" (2 Cor. 5:77(For we walk by faith, not by sight:) (2 Corinthians 5:7)). We see such faith exemplified in the lives of the Old Testament saints; as given in Hebrews 11. The Lord had often to rebuke His disciples for their want of faith in their daily walk. The believer should have faith in the living God concerning all the details of his daily life.
THE FAITH is at times referred to in the sense of “the truth;” that which has been recorded, and which the Christian has believed, to the saving of his soul. For this the Christian should contend earnestly; for it is fundamental; and many false prophets are gone into the world, and have even crept into association with the saints unawares (Jude 33Beloved, when I gave all diligence to write unto you of the common salvation, it was needful for me to write unto you, and exhort you that ye should earnestly contend for the faith which was once delivered unto the saints. (Jude 3)).

“Assurance” From Concise Bible Dictionary:

This word has in the Old Testament a different application from that which it has in the New Testament In the former it is “confidence or trust,” and agrees with the hopes of God’s earthly people in connection with the security in which Israel will dwell when restored to their land, when all their enemies shall have been put down by divine power: the effect of righteousness will be “quietness and assurance forever,” (Isa. 32:1717And the work of righteousness shall be peace; and the effect of righteousness quietness and assurance for ever. (Isaiah 32:17)): whereas in their disobedience they should fear day and night and have no assurance of their life (Deut. 28:6666And thy life shall hang in doubt before thee; and thou shalt fear day and night, and shalt have none assurance of thy life: (Deuteronomy 28:66)).
In the New Testament the Greek word πληροφορἰα implies “full assurance” and refers to eternal salvation. The gospel reaches a soul in power, and in the Holy Ghost and in “much full assurance” (1 Thess. 1:55For our gospel came not unto you in word only, but also in power, and in the Holy Ghost, and in much assurance; as ye know what manner of men we were among you for your sake. (1 Thessalonians 1:5)). We also meet with:
2. the full assurance of hope (Heb. 6:1111And we desire that every one of you do show the same diligence to the full assurance of hope unto the end: (Hebrews 6:11)), issuing in continued diligence of the saints in their work and labor of love: and

Strong’s Dictionary of Greek Words:

from 3982; persuasion, i.e. credence; moral conviction (of religious truth, or the truthfulness of God or a religious teacher), especially reliance upon Christ for salvation; abstractly, constancy in such profession; by extension, the system of religious (Gospel) truth itself
KJV Usage:
assurance, belief, believe, faith, fidelity