Why do they say the Son of God, when we also say he was God? Did he call himself God or The Son of God?
That's a great question. They say the Son of God because he used the term. In fact, Jesus favorite term that he used for himself wasn't Son of God, but rather Son of Man. If you read through the Gospels, Jesus rarely referred to himself by any other term than the Son of Man. That's probably for several reasons. If he had stood on a hillside and said, "Hear ye, hear ye, I'm God. Yep, I'm the one you've been waiting for. It's me. I'm the Messiah. I'm God. You may now commence worshipping me", he most likely wouldn't have made it off the hillside. He would most likely have been stoned on the spot. Thus ending the promising career of the Son of God.
Jesus' method was more subtle. The first mention of him being the Messiah, the Christ, the Son of God doesn't come from Jesus at all. It comes from others. In a conversation with Peter, Jesus asks, not tells Peter, "Who do people say I am?" After Peter enumerates the whole gambit of options folks were suggesting, he then follows up with a second question, "Who do you say I am?" That's when Peter, not Jesus, says, "You are the Christ". (the chosen one, the messiah, the savior, the Son of God) Jesus lead people toward the truth, but then let them figure it out for themselves.
He was the Son of Man because he was man. He was the Son of God because he was God. There was a separateness, because Jesus could pray to God, the Father. Then again, there was a sameness, because Jesus said, "I and the Father are one and If you have seen me, you have seen the Father. And Jesus forgave sins. When the Pharisees told him that only God could forgive sins, he didn't argue, he just responded by asking the question, "Is it easier to say your sins are forgiven or to say (to a man who couldn't walk) rise up and walk?". That's an easy one, but, of course, they refused to answer. He then followed up with, "rise up and walk", and the guy did.
Jesus just asked the question, but the answer was clear. Yes, only God can forgive sins. Yes, it's easier to say your sins are forgiven than get up and walk to a lame man. I just did both. Now, you do the math.
He said very plainly, "I am God" without ever saying it. Game. Set. Match.