They are the same being. Your logic is very flawed.
Scripture shows that as Jesus is the son OF God and not God himself and that the holy spirit is the spirit OF God and not God himself. I capitalized the word OF for a reason. Anyting that is FROM or OF something cannot be that something else. For example, I come FROM my mother, but I am not my mother. Jesus said, I come out FROM God. I came out FROM the father. Therefore Jesus came from God but is not God himself.
matt 28:19 Going, then, desciples all nations baptizing them into the name of the father, son and holy spirit. well this verse does not say the three form one God. They are all 3 mentioned in one verse and thats it.
1cor 8:6 There is only one God....The father.
1john 5:19 The son can do NOTHING of himself but what he sees the father do. Now if son can do nothing himself where is the trinity in that?
2john 6:38 For I come down from heaven, not to do my own will but the will of them that sent me. Now if Jesus was God he would be here diong his own will but he clearly stated he is not....... no trinity
john 4:34 Jesus said my meat is to do the will of him that sent me and to finish his work. Now did Jesus send himself? no God sent him.....So no trinity in that either
john 8:28 Jesus said, I do nothing of myself; but as the father has taught me. well Jesus does nothing himself but what the father taught him....So no trinity there.
john 12:49 For I have not spoken of myself; but the father which has sent me, He gave me the commandment what I should say and what I should speak. Now if Jesus was told what to say and speak by the father (GOD) trinity is completely impossible. no trinity there either.
There is so much more to prove they are not the same but im gonna stop here.