They are both in scripture BUT there is a difference!
DISPENSATION – a system of order, government, or organization of a nation, community, etc., especially as existing at a particular time.
COVENANT – Literally, a contract. In the Bible (see also Bible), an agreement between God and his people, in which God makes promises to his people and, usually, requires certain conduct from them. In the Old Testament, God made agreements with Noah, Abraham, and Moses.
1 Corinthians 9:17 For if I do this thing willingly, I have a reward: but if against my will, a dispensation of the gospel is committed unto me.
Ephesians 1:1 That in the dispensation of the fulness of times he might gather together in one all things in Christ, both which are in heaven, and which are on earth; even in him:
Ephesians 3:2 If ye have heard of the dispensation of the grace of God which is given me to you-ward:
Colossians 1:25 Whereof I am made a minister, according to the dispensation of God which is given to me for you, to fulfil the word of God;
Luke 1:72 To perform the mercy promised to our fathers, and to remember his holy covenant;
Acts 3:25 Ye are the children of the prophets, and of the covenant which God made with our fathers, saying unto Abraham, And in thy seed shall all the kindreds of the earth be blessed.
Acts 7:8 And he gave him the covenant of circumcision: and so Abraham begat Isaac, and circumcised him the eighth day; and Isaac begat Jacob; and Jacob begat the twelve patriarchs.
Romans 1:31 Without understanding, covenant breakers, without natural affection, implacable, unmerciful:
Romans 9:4 Who are Israelites; to whom pertaineth the adoption, and the glory, and the covenants, and the giving of the law, and the service of God, and the promises;
Romans 11:27 For this is my covenant unto them, when I shall take away their sins.
Galatians 3:15
Brethren, I speak after the manner of men; Though it be but a man’s covenant, yet if it be confirmed, no man disannulleth, or addeth thereto.
Galatians 3:17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.
Galatians 4:24 Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar.
Ephesians 2:12 That at that time ye were without Christ, being aliens from the commonwealth of Israel, and strangers from the covenants of promise, having no hope, and without God in the world:
Hebrews 8:6-10 But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. For if that first covenant had been faultless, then should no place have been sought for the second. For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah: Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord. For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people:
Hebrews 8:13 In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away.
Hebrews 9:1 Then verily the first covenant had also ordinances of divine service, and a worldly sanctuary.
Hebrews 9:4 Which had the golden censer, and the ark of the covenant overlaid round about with gold, wherein was the golden pot that had manna, and Aaron’s rod that budded, and the tables of the covenant;
Hebrews 10:16 This is the covenant that I will make with them after those days, saith the Lord, I will put my laws into their hearts, and in their minds will I write them;
Hebrews 10:29 Of how much sorer punishment, suppose ye, shall he be thought worthy, who hath trodden under foot the Son of God, and hath counted the blood of the covenant, wherewith he was sanctified, an unholy thing, and hath done despite unto the Spirit of grace?
Hebrews 12:24 And to Jesus the mediator of the new covenant, and to the blood of sprinkling, that speaketh better things than that of Abel.
Hebrews 13:20 Now the God of peace, that brought again from the dead our Lord Jesus, that great shepherd of the sheep, through the blood of the everlasting covenant