The word "manifest" is defined as "clear or obvious to the eye or mind." God's manifest presence is what believers see and know of Him. This is different from God's omnipresence. The meaning of the word omnipresence is "everywhere present." It is a key attribute of God. God is in all places simultaneously. There is no place where God's Spirit is not present. As David said,
What is the manifest presence of the Holy Spirit? How is it different from God's omnipresence?
"Where shall I go from your Spirit?
Or where shall I flee from your presence?
If I ascend to heaven, you are there!
If I make my bed in Sheol, you are there!
If I take the wings of the morning
and dwell in the uttermost parts of the sea,
even there your hand shall lead me,
and your right hand shall hold me" (Psalm 139:7–10).
God's omnipresence is not altered by the observer. He is there whether we know and see it, or not. Unbelievers may deny His existence, but that does not change the fact that He is omnipresent. God's manifest presence, on the other hand, is something that is sometimes experienced and other times not.
There are many examples of God's manifest presence in the Bible. God made Himself manifest to Moses in the burning bush (Exodus 3). God, the Son, was manifest to us in the person of Jesus Christ (John 1:14). The Holy Spirit was manifest to the believers at Pentecost (Acts 2:2–4). God's manifest presence appeared with Daniel and his compatriots when they were thrown into the fiery furnace because they would not worship Nebuchadnezzar's image (Daniel 3:24–25). Even King Nebuchadnezzar's eyes were opened and he saw the manifest presence of God.
The manifest presence of God is not necessarily, or even usually, something experienced empirically. That is, it cannot be felt by the senses or recorded by some physical means. But nonetheless, it is experienced. It is felt in the inexplicable comfort God gives in the midst of tragedy. It is experienced in answered prayer. It is experienced in changed lives.
The Holy Spirit is always with believers, indwelling us (1 Corinthians 6:19). He will never leave us (John 14:16). He is the guarantee of our salvation and our inheritance in Heaven (2 Corinthians 1:22; Ephesians 1:14). So the fact of His presence in our lives never changes, however our awareness of His activity in our lives might.
The difference between the manifest presence of the Holy Spirit and God's omnipresence is that God's omnipresence is always there, despite the fact that we cannot always feel it. In other words, God's presence is everywhere, at all times, and with all of us, believer and unbeliever alike. Likewise, His Holy Spirit indwells believers at all times. But His manifest presence is something that occurs in our lives as He chooses to reveal Himself. It is the occasional appearance to the human mind or eye of the reality of His omnipresence and continual care. "...for he has said, 'I will never leave you nor forsake you'" (Hebrews 13:5).
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Truth about the Holy Spirit