Isn't repentance just another word for faith? If someone were fighting and defending themselves in a brawl, aren't the words 'fighting' and 'defending themselves' describing different aspects of the same action? Likewise, I think Acts 20:21 show repentance and belief to be intrinsically related to the same attitudinal/belief event/process.
While defensive and offensive moves may fall under the umbrella of martial arts, they are done with different techniques and to accomplish different goals, though some of the goals overlap. Faith and repentance are different though they both fall under the umbrella of things God requires of man in order to receive the blessing of His promised salvation.
Faith is defined in Hebrews 11:1, "Now faith is the substance of things hoped for, the evidence of things not seen." Repentance is also defined in the Scripture, being found in Acts 26:20, Paul taught "that they should repent, turn to God, and do works befitting repentance". Faith is a foundation. Repentance is a turning. Both are necessary for conversion. Faith is generated by hope, but repentance is triggered by sorrow. "Now I rejoice, not that you were made sorry, but that your sorrow led to repentance. For you were made sorry in a godly manner, that you might suffer loss from us in nothing. For godly sorrow produces repentance leading to salvation, not to be regretted; but the sorrow of the world produces death. For observe this very thing, that you sorrowed in a godly manner: What diligence it produced in you, what clearing of yourselves, what indignation, what fear, what vehement desire, what zeal, what vindication! In all things you proved yourselves to be clear in this matter" (II Corinthians 7:9-11). Verse 11 is a beautiful summary of repentance: (1) diligent effort, (2) correction of past wrongs, (3) indignation, (4) fear, (5) extreme desire, (6) zeal, (7) vindication, and (8) proof of change. Faith is the foundation from which repentance is directed on its proper course, but they are not the same idea. They both lead to the same goal -- salvation, but they work on different aspects of a man's character and heart.
After writing the above, I thought to add the dictionary definition of repentance and faith. Looking up "metanoia" which briefly means "remorse, repentance, turning about, change of mind," I found this interesting paragraph in one dictionary, "Faith in Jesus is the basis for repentance (Mark 1:15). Faith is the positive expression of repentance: we turn to God through Jesus, God's representative. Repentance not only means a radical break with one's former life, but first and foremost it is a positive commitment to God's offer of salvation. To repent is to become a child of God (Matthew 18:1-3)." Faith, however, comes from the word "pisteuo" which briefly is defined as "believe, have faith in, convinced of, trust, rely on, have confidence in." I know of no dictionary that lists "metanoia" as a synonym of "pisteuo". The same dictionary had this interesting note, "Pisteuo often means 'to receive' the message of Jesus; to believe in Him as the Son of God; and, through the Spirit's work, to submit to His saving will (Mark 1;15; John 1:12; 3:16; 6:29; Acts 4:4; 10:43; I Corinthians 1:21; Galatians 3:22; I Timothy 3:16; I John 3:23). Closely related to this is the 'obedience of faith' (Romans 16:26; cf. 1:5). To obey is to believe the gospel (Romans 10:16; cf. 15:18)."
While faith and repentance are interactive, they are different things that lead to the same goal -- just as hearing the gospel, confessing Christ, being baptized into His death, and living an obedient life are all interactive ideas that are different. None can stand alone because each affects a different part of man's character. None are unnecessary as each alters the person in subtly different ways to effect the creation of a child of God.
[Dictionary references come from The Complete Bible Library: Greek English Dictionary.]