Is this same faith? No. It's religious debates. This means anyone can join.
I am a syncretist. Something Muslims would probably consider haram because they don't believe in questioning ideas or mixing with other people.
By your own words, you have admitted that Allah is not God, something Muslims are always careful to tell "nonbelievers" is not so. "Oh we worship the same God as you," they all say. Thank you for reminding me otherwise.
God is named God, because he is God. Any God who needs another name, is in question after all:
"The tao that can be told is not the eternal Tao, the name that can be named is not the eternal Name. "
Once you start putting a name to God, calling God something fixed like Emily or Joseph or Ashley or Bob (or Allah), you turn your deity into lowercase god. An idol. Just as you do when you you start kneeling several times a day to a stone made by human hands. Muhammad didn't abolish idol worship. He streamlined it! That makes him a false prophet, and our discussion could technically be over.
But debates are not things to be won, because winning doesn't reallt help anyone actually reach an understanding. So here it is. What makes a prophet different from say... a camel salesman looking to pretend to be one, by claiming an angel spoke to him? There are several things: (1) Outside authority, (2) motive, (3) mission.
(1)
You cannot be a self-proclaimed prophet. To be a prophet implies that God chose you. And you will see this repeatedly in the Jewish and Christian Old Testament but also in leaders of Hindu and Buddhist traditions where avatars or orher messengers spoke to them. If the Quran is written by Muhammad himself (which is, in essence so, though actually you can tell he orated it because of repetition frequent within the text
https://www.quora.com/Is-Quran-written-by-prophet-Muhammed-alone )
then he is a self-proclaimed prophet. Why is it important that a prophet not be self-proclaimed? Because it not only draws into question their motives, but leads to a sense of "because I said so." You'll see repeatedly that prophets in Judaism are never self-proclaimed, in fact Jonah proves this extemely well, when he is called by God and he runs away to another country. He is called to tell Ninevah, a section of I believe in Iraq, that their way is in error. Okay picture this, a Jew told to tell Iraqis, "God wants you to repent." Yeaaah, most people will run the other way. But it turns out Jonah isn't afraid that they will try to kill him, no he is afraid they will in fact put on sackcloth and repent. He hopes God would kill off these people that he probably dislikes but knows they would repent if someone like him told them. What does this teach us but that a prophet doesn't call himself but rather receives a call, and like or not, he feels driven to do so ( Jonah in fact tried to flee to another country and got tossed overboard after they decided he was cursing the ship).
(2) A prophet also cannot be motivated by greed (and again, prophet in this case is not one who is a seer, but one who has been instructed to deliver a message). If a prophet is after fame, power, or wealth their motives are wrong and their words cannot be trusted.
HISTORY OF MUHAMMAD
Muhammad was a child of a merchant family adopted into a caravan. He starts retreating into a mountain and sees a... stop right there! Already we have his motive. He is sick of the caravan life and wandering in poverty, he doesn't want to be some unknown trader, so he starts coming up with a story about how some angel talked to him. We already have a motive of fame, and through his life history we also see wealth and power. He dies fairly well off. Contrast this to the fate of most Jewish prophets. Most of them were outcasts, penniless, and some died in the most painful way imaginable. I could talk about Jesus, but I know the story that Muslims hear about Jesus, so that's pointless. Let's talk about Jonah again. What did he get for his trouble? Fame? Wealth? Nope, he got to sit outside the city while all of the others had become righteous and were in atonement, and watch a tree wither while he suffered in the sun. The text ends with him getting lectured. Many of the other prophets got killed for their efforts. Elijah had to run to a mountain somewhere because the kings and leaders found his message offensive. Not one of these people did it for the money or for fame, but rather suffered for their message.
(3) And yet, what defined a prophet was a sense that when times got hard, they knew exactly what they were told to do. Here again, Muhammad fails. Having been rejected by the people he tries to convert, he decides to make wae on them. This here invalidates him finally, and completely as a prophet. When a prophet abandons their mission to spread a message and instead visits violence on the people called to hear it, he has failed in his mission. Any real prophet would have told him exactly what to do. To be unswayed by their rejection, and stay to proclaim his words anyway, accepting whatever they did to him. But instead, he makes war on his charges.
Not one of the prophets of Judaism does this. They carry out their mission regardless of person risk. They try to reform injustices, to make converts even when those around them hate them or distrust them, and they stay on task, not ababdoning their way to violence.
Jesus actually never once called himself Son of God. He called himself the son of man, a name from Ezeki mostly. It was his disciples (Peter in particular) and his enemies (one of the Roman centurions who witnessed a storm during his death) who said he was the Son of God.
Jesus in his own lifetime is asked by whose authority. So instead he asks about John the Baptist, whether he acted by God's authority or by man's (that is, his own). John the Baptist, if he was a prophet would have acted by God's authority, for reasons I have told in the paragraphs above. Yet the Pharisees were reluctant to admit he was a prophet because John personally damaged their reputation because he was not like them, and it also raised the quedtion of why as priests they rejected him. On the other hand, they feared the crowd if they said that he was not a prophet. So they were trapped. Because they couldn't answer there, Jesus didn't have to answer, because like John he had also been rejected by the priests of his time.
