What is the difference between God and the Spirit of God? What is the difference between Christ and the Spirit of Christ? What is the difference between the Father and the Son?
We could go on and on. If we understood this perfectly, we would be God and that is untrue so we can never understand this question finally.
The church fathers simply asserted (in their desperation to say something) that all three are of the same substance but different in function. I am unaware of any better (although hopelessly inadequate) statement.
The Bible is far more interested in explaining the Character of God as loving, kind, gracious but just (and outour need to emulate that Character). It makes almost no attempt to explain the substance and makeup of God but simply asserts God's existence: "In the beginning God ..." Gen 1:1.
The closest the Bible comecomes to explaining anything about God is "God is Spirit"; but in reality, that tells us very little.