As you say the Christians believe the Holy Spirit in
Acts of the Apostles 2:1-4 to be the same Holy Spirit Christ talks about in the gospel of John.
The Holy Spirit descended upon the disciples at Pentecost but that is a separate event from the Comforter being sent later. They were empowered to go out and proclaim the gospel Jesus had taught them. They weren't being told something new that they couldn't bear to hear when Jesus was still alive. What makes more sense in reference to the Comforter is a new Revelation from God according to the more advanced capacity of people in the future to receive that message. The Gospel of Jesus was not suited to the capacity of the Hebrew people at the time of Moses. The revelation of God through Moses is what the Hebrew people needed 3 1/2 thousand years ago.
Lets look at those verses in the Gospel of John more closely .
John 16:12-14 I have yet many things to say unto you, but ye cannot bear them now. 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. He shall glorify me: for he shall receive of mine, and shall shew it unto you.
So if it was 'all truth' they could not near to hear, why were not ready for 'all truth' at that time? That description best fits a future Messiah or Christ who reveals 'truths' that the disciples of Christ were not ready for at that time. Of course 'all truth' can't literally be all truth so meant relative to what Christ taught.
Jesus was “a Comforter” because Jesus brought the Holy Spirit. Muhammad is another Comforter and also had the Spirit of truth.
John 14:16 And I will pray the Father, and he shall give you
another Comforter, that he may abide with you for ever;
John 14:17 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.
It is the Comforter who fulfils these verses in John, not the Holy spirit at Pentecost spoken in Acts.
John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name,
he shall
teach you all things, and
bring all things to your remembrance, whatsoever I have said unto you.
John 15:26 But when the Comforter is come, whom I will send unto you from the Father, even the Spirit of truth, which proceedeth from the Father,
he shall testify of me:
John 16:8 And when he is come,
he will reprove the world of sin, and of righteousness, and of judgment:
John 16:13-14 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. He shall glorify me: for he shall receive of mine, and shall shew it unto you.
The Apostle John was a prophet of God. He was a prophet of God
before Pentecost as well as afterwards. We know this because Jesus said he was like the prophet Elijah. (Matthew 17:11, Luke 1:17, Malachi 4:5). In that sense John the Baptist was like a prophet of God in the Hebrew Bible. This is unrelated to the descent of the Holy Spirit at Pentecost in Acts of the Apostles 2.
Paul is certainly a good example of one who was enabled by the Holy Spirit. Although Paul converted some years after Pentecost it is reasonable to attribute His experiences to the Holy Spirit that clearly manifested at Pentecost. However, Paul provided interpretation of the Teachings of Jesus, so didn't really teach anything new that the disciples couldn't cope with at the time Jesus was alive. He simply reframed the Message of Jesus for both the Gentiles and Jews.