In the Bible, Holy Spirit is God and Gabriel is His Angel so they are different. There are three different angel mentioned in the Bible; they are Gabriel the messenger angel, Michael the warrior angel, and Satan the fallen angel. Muhammad had a little knowledge about Tanakh and the New Testament the reason he erred in identifying Holy Spirit and Angel Gabriel.
Catholicism, the religion founded by Jesus, defines the word “holy” as pure, perfect, or sinless. Therefore, only God could take this attribute because He is the only perfect being. God is naturally spirit, and He is holy too that’s why He is called “Holy Spirit” in other title. Jesus is also called “holy” [Luke 1:35] or “perfecter” because he’s an amount of spirit emanated from God (the Father). So if Jesus (the Son), the Holy Spirit, and the Father have the same attributes, it means they are one nature. In Catholic teaching, Muhammad cannot be called holy because he’s a very sinful man (polygamist, murderer, rapist, robber, etc.). He’s one of those who will be thrown into the fiery lake on the Judgment Day. Ironically, though Muslims denied the deity of Jesus, their Quran also testifies that Jesus is spirit or word proceeding from Allah [Surah 4:171, 66:12, 21:91, & 3:45]. A spirit of God is different from a created spirit, thus to say Jesus is a spirit of God, it means He is God Himself. Since there are many type of spirits (God, angel, soul, thought, energy, and others), the word “holy” is attached to the word “spirit” so that to mean divinity, that the spirit mentioned is referred to the divine spirit.
IN RESPONSE TO THE TRINITY DOUBTER:
Since God or the Holy Spirit sent forth His spirit (Psalm 104:30), He became the source spirit (the Father) of the sent Spirit (the Son) [Psalm 2:7]. Jesus is not a biological son of God as what Allah believes, but He is the emanated Spirit coming from God (the source). The Bible says the the Son is the radiance of the Father’s glory, and the upholder of all things [Hebrews 1:3]. When we say Satan is the father of lies, it means he is the source of lies, and not the biological father of lies.
The problem of our Muslim brothers is they thought that when God came to the world, He left His abode and brought His whole being to Earth. So when Jesus died there was no more God. But it is not the case, because God is not human which has limited resources. He is extremely vast [Isaiah 66:1], He could pour His spirit upon all flesh [Joel 2:28 & Ezekiel 39:29]. He could send His spirit [Isaiah 48:16]. Keep in mind that God is everywhere, He covers the whole universe. In fact, this is the reason why all the heavenly bodies are floating in the empty space because God upholds them [Hebrews 1:3].
Jesus told us that after Him, He will send a Spirit of the Truth (Holy Spirit), He says; “When the Counselor comes, whom I will send to you from the Father, that is the Spirit of truth who goes out from the Father, He will testify about Me [John 15:26]. Notice also that Jesus has the power to send a spirit from the Father so he is almighty. This Spirit of Truth will testify about Jesus, but referring to [John 8:18], Jesus is the one who will testify about Himself. He says, “I am the one that bear witness of myself, and the Father that sent me bear witness of me“. Therefore, the Holy Spirit (Spirit of Truth) to be sent by Jesus is also Himself. And since Jesus is also the Father [Isaiah 9:6], these three are one _the Trinity. Kindly read the supporting verses;
[Isaiah 9:6] For a child will be born to us, a son will be given to us; And the government will rest on His shoulders; And His name will be called Wonderful Counselor, Mighty God, Eternal Father, Prince of Peace.
Jesus confirmed Isaiah 9:6 by declaring He and the Father are one [John 10:30].
[Isaiah 48:16] also prophesies that an ever existent being is sent by the Lord God and His Spirit. It says; “Come near to Me, listen to this: From the first I have not spoken in secret, From the time it took place, I was there. And now the Lord GOD has sent Me, and His Spirit.”
Jesus confirmed Isaiah 48:16 by telling He came down from Heaven and sent by the Father [John 6:38].
Jesus also said that those who have seen Him, have seen the Father. And He is in the Father and the Father is in Him [John 14:9-10] _implying that He is God Himself because they are one with the Father.
The Trinity are one, so they are equal. The arrangement, “the Father, the Son, and the Holy Spirit” has symbolism. It symbolizes the three significant stages of God’s appearance to mankind. First, the Beginning period, in which God introduced Himself to mankind as the creator. Second, the Salvation period, in which God introduced Himself to mankind as a savior. And third, the Judgment period, in which God will introduce Himself to mankind as a Judge.
Jesus serves as our purifier or perfecter, the Salvation sent by God [Isaiah 56:1 & Luke 2:29-30]. “Jesus” is an English transliteration of the word ‘Iesus’, a Greek transliteration for Hebrew ‘Yeshua’ which means “God saves” or “God’s Salvation”. Because of His purity, He can purify those who believe His redemptive work and follow His will. Adam and Eve sinned, mankind lost their eternal life [Genesis 3:23] because the penalty of sin is death [Proverbs 10:16 & Romans 6:23]. And this is what we inherited as heirs of Adam and Eve, the death, for we are born sinners [Psalm 51:5 & 58:3].
Mankind can only regain their eternal life by becoming pure again. But who can bring the pure from impure? It is God alone [Job 14:4]. God is holy, His abode is holy, no sinners can enter there [Revelation 21:8].
Also read: THE MYSTERY OF TRINITY FATHOMED