getting back to the original question of the thread...
As with many things, the answer depends on your definitions and assumptions. Let’s start with Islam. If you’re a believer in it, then you would never say it’s a sect of Judaism or Christianity. You would believe that the Koran as revealed to Muhammad is the true word of God restored, while the scriptures and accompanying beliefs of Christians and Jews were corrupted over time. That accounts for a certain amount of respect for them compared to idolaters, as “People of the Book”, while still regarding them as infidels. If you don’t believe in Islam, then the more accurate way to put it would be that he heard teachings of the other two and borrowed and synthesized and built on them.
As far as “Christianity” it also depends on your definition. If you mean the church-i-anity understood and practiced by many or perhaps most of the people filing into churches every Sunday, I might be inclined to agree with you that it’s the same as any other religion. It’s “go to this building, say these words, endure these rituals, do these good things, and don’t do these bad things, in order to earn the rewards in this life and the next.” You could just substitute deities and rituals. Then it could be not only Judaism or Islam, but any number of other religions. The moral teachings are more or less the same. We all pretty much know what’s good and what’s not. I call it conscience, a humanist would have some other name and explanation for it.
On the other hand, what the Bible actually teaches, what Jesus actually established, is unique. It is different from all of the religions of the world, including the one that masquerades in its name. It is not a religion, but a relationship. It is not based on me doing things to try and earn a reward from God. It’s about how he proved his love for me by becoming vulnerable in order to take away what was keeping us apart in the only way it could have been: by Him Himself suffering and dying. He nailed the law to a tool of execution and killed it. I am now unconditionally forgiven for all of the ways I fail to live up to it.
Yes I try to do right things and not wrong ones as a result, but not to get a reward, or because I think he’ll be mad at me if I don’t, or even because I think I should. I do them because they are the things that make me better able to know Him, and to know about Him, which is not the same thing, and to become like Him. I do them because they are the things He loves and I want to make Him happy. I do them out of a gratefulness for what He’s done, which is growing into a love for who He is, as I come to know Him better and see Him clearer.
I hope this is helpful.