New Testament scholar Gordon Fee has made a case for what he calls "the presence motif" as the core thematic river that runs through the Christian theistic Grand Narrative. From Genesis to Revelation, the point of the whole thing is God and his empowering presence. (See, e.g., Fee, God's Empowering Presence: The Holy Spirit in the Letters of Paul.)
Fee defines "Holy Spirit" as "God's Empowering Presence." I like this. But God's presence is this and more. God's presence is his all-encompassing Trinitarian being; viz., the three-in-oneness of Father, Son, and Spirit. Wherever God manifests himself, he is there in his totality. When God is among us, the Father does not leave the Son and the Spirit in heaven.
Because of this, what I am calling a Presence-Driven Church is vaster than a Spirit-led Church. "Spirit-led" is subsumed under "Presence of God." "Spirit-led Church" is necessary but insufficient to describe "Presence-Driven Church." (Like having three sides is necessary but insufficient in describing a triangle. That's just an explanatory analogy. In no way do I think a triangle is a good analogy for the Trinity.)
By "Presence-Driven Church" I mean a community of Jesus-followers whose doing is "driven" by God, presently. This involves all of God - Father, Son, Spirit. The Presence-Driven Church finds its "doings," its raison d'etre, in its relational connectedness with the Trinitarian being of God. Which includes, of course, the power of the Holy Spirit.
(For more see my book Leading the Presence-Driven Church.)