“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. 32:20; Hab. 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. 15:6). 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 3:36). 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. 2:8). Salvation is on the principle of faith in contrast to works under the law (Rom. 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 2:14-26). 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. 5:7). 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 3).
“Hope” From Concise Bible Dictionary:
This is described as waiting for something that is not seen but which has been promised. Rom (8:24-25). Blessed is the man whose hope the Lord is; though troubles arise he will not cease to bear fruit (Jer. 17:7-8). There is nothing vague in the Christian’s hope: it is an anchor of the soul, sure and steadfast, because the Lord Himself is his hope, and Christ in him is the hope of glory (Col. 1:27; 1 Tim. 1:1; Heb. 6:18-19). The coming of the Lord, and not death, is a blessed part of the Christian’s hope (1 Thess. 4:13-18; 1 John 3:2-3).
Strong’s Dictionary of Greek Words:
Meaning:
from a primary ἔλπω (to anticipate, usually with pleasure); expectation (abstractly or concretely) or confidence