According to this
UPCI Pentecostal website, they believe that our Father in heaven is God, and that Jesus is God, and that the Holy Spirit is God, and that they are one God. This is also good, orthodox Catholic belief so far.
But the Catholic Church says that the Father, Son and Holy Spirit are three persons; the UPCI says they are the same person.
Consider John 8:13-18 (New International Version)
[sup]13[/sup]The Pharisees challenged him, “Here you are, appearing as your own witness; your testimony is not valid.”
[sup]14[/sup]Jesus answered, “Even if I testify on my own behalf, my testimony is valid, for I know where I came from and where I am going. But you have no idea where I come from or where I am going. [sup]15[/sup]You judge by human standards; I pass judgment on no one. [sup]16[/sup]But if I do judge, my decisions are right, because
I am not alone. I stand with the Father, who sent me. [sup]17[/sup]In your own Law it is written that the testimony of two men is valid. [sup]18[/sup]I am one who testifies for myself; my other witness is the Father, who sent me.”
Jesus said that He is not alone, because He is with His Father. If they were the same person, then the presence of the Father would not make Him any less alone. Jesus said that His testimony and His Father’s testimony are two testimonies. But if they were the same person, that would be just one testimony.
Consider
1 John 5:7 (from the King James version of the Bible, the version the UPCI uses):
For
there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and these three are one.
God is both a Trinity and a unity, as the Catholic Church teaches.
When Jesus was baptized, God the Father said “This is My beloved Son”. He did not say, “It is I Myself Whom you have just baptized”. The Father goes on to say “in whom I am well pleased”, which would sound narcissistic, if He were talking about Himself.
At the Last Supper, Jesus said “And I will pray the Father, and he shall give you another Comforter, that he may abide with you for ever… 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.” Jesus said that the Holy Ghost is “another Comforter”, not the same as Himself. Moreover, Jesus asks the Father to send the Holy Ghost, if they were all the same person, neither the asking nor the sending would make sense, our Lord would just do it Himself.
The persons of the Most Holy Trinity always act in perfect accord, but the Church has understood from her beginning that they are distinct persons.
Here is an article on the subject from Catholic Answers.