Both.
Disclaimer: I have a very unorthodox view of the Holy Spirit. I mean that by both the standards of "orthodox" Christians and even Unitarians. And my view isn't really comprehensible, either by others or myself. So here we go.
We start with Genesis 1:2.
[Genesis 1:1-2] In the beginning of God's preparing the heavens and the earth -- the earth hath existed waste and void, and darkness is on the face of the deep, and the Spirit of God[וְר֣וּחַ אֱלֹהִ֔ים] fluttering[מְרַחֶ֖פֶת] on the face of the waters, (YLT)
I like how Young's Literal Translation renders מְרַחֶ֖פֶת(see Strong's H7363) as "fluttering". The word appears in two other places in the Hebrew Bible, which are Deuteronomy 32:11 and Jeremiah 23:9. In the former, the word is used to describe how God, like an eagle that flutters above her young to care for them, spreads her wings over them to catch them if they should fall, watched, cared for, and instructed Jacob. This is clearly a personal action, one performed by an animate entity. And in the other occurrence in Jeremiah 23:9, מְרַחֶ֖פֶת is translated as "shake" or "tremble". Essentially, the word refers to a sort of energized, quivering motion, and in the case of Deuteronomy 32:11, one that is intimate. I believe the word is being used in such a manner in Genesis 1:2. Ruach Elohim[וְר֣וּחַ אֱלֹהִ֔ים] is energized, in a quivering motion above the face of the dark, chaotic waters; like an eagle intimately fluttering over her young, the Spirit flutters over the deep abyss, ready to transform it and create an ordered reality. It is the Spirit that does this, and yet, it is God who prepares the universe(outer space, atmosphere, and land, according to ancient Hebrew cosmology), as we are told in Genesis 1:1. Indeed, God has operated His invigorated Spirit so as to bring order into the dark, turbulent cosmos. What is this Spirit of God? Well, the Hebrew word for "spirit", ר֫וּחַ(see Strong's H7307), pronounced ruach, is quite a word, to say the least. It has various uses. It can refer to wind, breath, cool air, a blast, a vital, animating force, a supernatural, immaterial being, or even someone's mood, disposition, or mind! Indeed, quite a word! If I could summarize what the word ר֫וּחַ refers to in one expression, it would be this; that which is insubstantial, that is, without visible or concrete form, but can be felt, perceived, or discerned, whether directly or indirectly(through its effects).
So, what is the Ruach Elohim[וְר֣וּחַ אֱלֹהִ֔ים], or Spirit of God? Can we really answer that question? Perhaps not in any distinct, definite way, no matter how each of us would like to. Should that surprise any of us? Is God so simple and straightforward that He can be comprehended in His entirety? Or is God infinitely more complex than anything we could ever understand, that is, unfathomable and ungraspable? I think so.
Now take a look at this:
Luke 11:20 But if it is by the finger of God that I cast out demons, then the kingdom of God has come upon you.
Matthew 12:28 But if it is by the Spirit of God that I cast out demons, then the kingdom of God has come upon you.
It is the exact same situation, and Jesus calls God's Spirit His "finger". How is the Spirit of God ... His finger? This analogy teaches us a lot about God's Spirit.
Someone's finger is an extension of them; of their being. If I touch you with my finger, I don't say that my finger touched you(even though that is literally what happened); I say that I touched you. Is my finger literally me? No. And yet, it represents my entirety. Why? Because it is an extension of me; an important part of me. Now say my wife tells me to put some dirty laundry in the washer, and I pick up the laundry with my hands and stuff it in the washer with my hands. I don't say to her, "my hands picked up the laundry." I say to her, "I picked up the laundry." The work of my hands IS the work of me because my hands ARE me. My hands are an extension of me, and thus they represent my totality, even though they aren't identical to my totality. What my hands do is what I do. If you are in the presence of any of my body parts, you are in the presence of me. If you are touched by any of my body parts, you are touched by me. To be in the presence of an extension of my totality is to be in the presence of my totality. If you are touched by an extension of my totality, you are touched by my totality. However, I don't say that my finger(or arm, or any extension of me) is an entirely distinct conscious entity who is fully me but also not me simultaneously. That's nonsense and logically impossible(I'm looking at you Trinitarians =)).
This is why Jesus could say stuff like this:
Matthew 18:20 For where two or three are gathered together unto My name, there am I in their midst."
Jesus is not literally in our midst when we are gathered in His name! He is in Heaven, and has yet to return! And yet, here Jesus is telling us that He IS in our midst when we are gathered in His name. How is this possible? Through His Spirit, His Ruach(ר֫וּחַ). It IS Him; His essence, His presence, a fundamental part of His very being/totality/entirety. It is an extension of Jesus, one that can reach a group of believers no matter where they are in the world, such that He is, essentially, in their very presence, and they in His! Christ's Spirit is extended, that is, stretched forth by Him, so that His people can feel His presence and become empowered by it to perform all sorts of works, receive all sorts of gifts, bear all sorts of fruits, etc. And, of course, we can FEEL God's Spirit; His essence or presence. Remember, the word ruach(ר֫וּחַ) denotes something insubstantial that can be felt or perceived. God's Spirit is not something imperceptible or indiscernible. We can feel Jesus' presence with us when we gather in His name. We can feel God's Spirit dwelling in us when we walk with Him and live by His commands and principles, and reflect His image, Christ, in our day-to-day lives. Christ's Spirit is very personal. It is not simply a "force" or "energy" or "power".
And it is why John could say things like this:
1 John 4:15 Whoever confesses that Jesus is the Son of God, God abides in him, and he in God.
Does the Almighty, Sovereign Creator of the Universe literally abide in us? No, of course not. But also He does, according to John. How?
1 Corinthians 6:19–20 Or do you not know that your body is a temple of the Holy Spirit within you, whom you have from God? You are not your own, 20 for you were bought with a price. So glorify God in your body.
To have God's Spirit within us is to have God within us because the Spirit is "from God"; it is His presence, His essence, His breath. We can feel it! How would I describe the Holy Spirit? As the DNA of God, an extension of His eternal being, that God uses to accomplish all He wills, and that He imprints on His creation in various manners. He imprints His Spirit on His people so that they have different gifts such as gifts of healing or prophecy or speaking in tounges, teaching, evangelising, etc.(see Romans 12:6-8, 1 Peter 4:10). And He imprints His Spirit on His people so that they can bear certain fruits, such as love, peace, kindness, etc.(see Galatians 5:22-23). And so it is both the Spirit and God that gives gifts to believers and bears fruit through them.
Because the Holy Spirit is God's "DNA", an extension of His very being, His fundamental essence, anything that can be attributed to the Holy Spirit can be attributed to God, and vice versa. This should include "apportioning", "distributing", and "willing".
And so my answer to your question would be ... the Holy Spirit distributes spiritual gifts because God distributes spiritual gifts, and God distributes spiritual gifts because the Holy Spirit distributes spiritual gifts. The Holy Spirit "wills" insofar as God wills, and God wills insofar as the Holy Spirit wills. The Holy Spirit is grieved insofar as God is grieved(see Ephesians 4:29-32). And we lie to God because we lie to the Holy Spirit(Acts 5:1-5). This does not make the Holy Spirit a conscious entity distinct from God but also fully God simultaneously, as the Trinity doctrine asserts.
Perhaps my interpretation is not satisfying enough. That makes sense. People aren't usually satisfied by things they don't fully understand. It's very easy to say that the Holy Spirit is a person because we understand what a "person" is; we want to say that the Holy Spirit is a person because we want to understand the Holy Spirit. Contrariwise, it's very easy to say that the Holy Spirit is an impersonal "force" or "power", because we understand what forces and powers are; we want to say that the Holy Spirit is just a force or power because we want to understand the Holy Spirit. That's why 99% of people fall into one of two camps; the "Holy Spirit is a person" camp or the "Holy Spirit is an impersonal force/energy" camp. I suggest that God is vastly more complex than anything we can imagine, such that it is impossible to simply reduce the Holy Spirit to either a "person" or "force". But hey, that's just me.
Hope this helps! Have a good day! :)
P.S. I believe the Holy Spirit can be referred to by either an impersonal pronoun(it) or a personal pronoun(he). I choose not to refer the the Spirit as a "he" because it automatically makes people assume I am a Trinitarian. However, I have no problem with others calling the Holy Spirit a "he". I think referring to the Holy Spirit as an "it" or "he" is justifiable.