What is "spirit" in Holy Spirit? Jesus taught the woman of Samaria that "God is spirit".

The answer to the Penny Catechism Q17. What is God? is God is the supreme Spirit, who alone exists of himself, and is infinite in all perfections.

As the Third Person of the Blessed Trinity, the Holy Spirit is God and consubstantial with the Father and the Son.

A diagram as one below is sometimes used to explain the mystery of the Blessed Trinity.



This is where it gets confusing for me. If each of the persons is God, then from the foregoing we can say


  The Holy Spirit is the supreme Spirit.


Since the Father and the son are each also the supreme Spirit but not the Holy Spirit, what is "spirit" in the Holy Spirit and how is it different from "spirit" in the supreme Spirit?

Catholic perspective preferred but any others welcome from Christians who believe in the Blessed Trinity.
What is “spirit” in Holy Spirit?

Spirit = pneuma

Vines definition

primarily denotes the wind" (akin to pneo, "to breathe, blow"); also "breath;" then, especially "the spirit," which, like the wind, is invisible, immaterial and powerful.

What can be confusing is that the word "spirit" can be used in different ways.

God is called a spirit to differentiate him from the material world.


  John 4:24  God is a Spirit: and they that worship him must worship him
  in spirit and in truth.


There is a person in the Godhead that is called the Holy Spirit because the work he does is similar to receiving a breath of inspiration. Both Jesus and God send forth the Spirit.


  John 14:16-17  And I will pray the Father, and he shall give you
  another Comforter, that he may abide with you for ever;  Even the
  Spirit of truth; whom the world cannot receive, because it seeth him
  not, neither knoweth him: but ye know him; for he dwelleth with you,
  and shall be in you.
  
  John 16:13  Howbeit when he, the Spirit of truth, is come, he will
  guide you into all truth: for he shall not speak of himself; but
  whatsoever he shall hear, that shall he speak: and he will shew you
  things to come.
  
  John 20:22  And when he had said this, he breathed on them, and saith
  unto them, Receive ye the Holy Ghost:


There is a function of the Holy Spirit as one by whom new life is imparted.


  John 6:63  It is the spirit that quickeneth; the flesh profiteth
  nothing: the words that I speak unto you, they are spirit, and they
  are life.


The Holy Spirit is a spirit in that he is not of the material universe. He is also a spirit in that he leads us and teaches us by inspiration similar to receiving life giving breath. He is also a spirit because of our new life in Christ (our spiritual life) is made possible through his quickening.