I think the difference is that the majority of all other faiths believe in God, they believe that God created the heavens, the earth and everything we have. The problem is that even though they believe this, they believe that others should be worshipped along with God.
So polytheists believe in the Creator too, however they believe that the idols they worship/pray to etc are intermediaries between them and God. If they pray to these idols, its a form of associating partners to God because if God is the All-Hearer, then why not pray to Him Alone anyway?
And your Lord said: "Invoke Me, [i.e. believe in My Oneness (Islâmic Monotheism)] (and ask Me for anything) I will respond to your (invocation). Verily! Those who scorn My worship [i.e. do not invoke Me, and do not believe in My Oneness, (Islâmic Monotheism)] they will surely enter Hell in humiliation!" [Qur'an 40:60]
If thou ask them, who it is that created the heavens and the earth. They will certainly say, "Allah". Say: "Praise be to Allah!" But most of them understand not. [31:25]
If indeed thou ask them who has created the heavens and the earth and subjected the sun and the moon (to his Law), they will certainly reply, "Allah". How are they then deluded away (from the truth)? [29:61]
Is it not to Allah that sincere devotion is due? But those who take for protectors other than Allah (say): "We only serve them in order that they may bring us nearer to Allah." Truly Allah will judge between them in that wherein they differ. But Allah guides not such as are false and ungrateful. [39:3]
That's what all other people who believe in God do. We don't believe God has children because He doesn't have to. And if someone says that God can do anything, then you have to ask them if God can lie? Or the simple argument by the philosophers; can God make a rock so heavy that no-one can pick it up? The answer to this is simple, God only does what befits His majesty.
Had Allah wished to take to Himself a son, He could have chosen whom He pleased out of those whom He doth create: but Glory be to Him! (He is above such things.) He is Allah, the One, the Irresistible. [39:4]
All worship is due to God Almighty, and Allaah is what the arabs call God, so its nothing new, even the christian arabs call God, Allaah.
Our testification of faith is that there is none worthy of worship [i.e. of being divinely obeyed, prayed to, worshipped etc.] besides God Alone, and that Muhammad (peace be upon him) is God's Final Messenger.
And verily, We have sent among every Ummah (community, nation) a Messenger (proclaiming): "Worship Allah (Alone), and avoid (or keep away from) Taghut (all false deities, etc. i.e. do not worship Taghut besides Allah)." Then of them were some whom Allah guided and of them were some upon whom the straying was justified. So travel through the land and see what was the end of those who denied (the truth). [Qur'an 16:36]
So all prophets actually called to the worship of God Alone, without no associates. So we dont believe God is in three parts, or that God should be contacted through stone idols.
This (Quran) is a Message for mankind (and a clear proof against them), in order that they may be warned thereby, and that they may know that He is the only One Ilah (God - Allah) - (none has the right to be worshipped but Allah), and that men of understanding may take heed.
And Allaah Almighty knows best.