What is the difference between God and the Spirit of God?

There are passages that appear to establish an identity between God and his Spirit: > 24 **God is spirit**, and those who worship him must worship in spirit and truth.” [John 4:24, ESV] > 17 Now **the Lord is the Spirit**, and where **the Spirit of the Lord** is, there is freedom. 18 And we all, with unveiled face, beholding the glory of the Lord, are being transformed into the same image from one degree of glory to another. For this comes from **the Lord who is the Spirit**. [2 Corinthians 3:17-18, ESV] However, other passages appear to make a distinction between the two, as if God and his Spirit were different beings. The passage that is most clear in this regard, in my opinion, is 1 Corinthians 2:10-13: > 10 these things **God has revealed to us through the Spirit**. For **the Spirit searches everything, even the depths of God**. 11 For who knows a person's thoughts except the spirit of that person, which is in him? So also **no one comprehends the thoughts of God except the Spirit of God**. 12 Now we have received not the spirit of the world, but **the Spirit who is from God**, that we might understand the things freely given us by God. 13 And we impart this in words not taught by human wisdom but taught by the Spirit, interpreting spiritual truths to those who are spiritual. [1 Corinthians 2:10-13, ESV] So, on the one hand, God is Spirit, but on the other hand, God has a Spirit. Does this mean that God is Spirit and has a Spirit simultaneously? Is there any difference between God and his Spirit? How can we make sense of all this?