Question, are all segments/divisions, etc. of Freemasonry under the same belief systems or do they have their unique set of beliefs that correlate with one another?
That's an oddly worded question so I can't tell what you intended to ask. I'm going to guess it's a question about religion.
We require a belief in a supreme being so we are all men of faith. Then we forbid discussion of sectarian religion in our meetings. As a result we never learn the religious membership of many. We know that we have Brothers of every religion you have ever heard of and many you haven't. There is no way to know the amount of religious diversity in your own lodge but it's usually broader than you dream.
The York Rite has several groups of degrees. One of them requires members to promise to defend Christianity. The exact requirements vary from state to state so you can't assume every member of the Commandery are Christians but most are. It's the only order in the Americas with anywhere near a requirement of a specific religion.
Our embracing free choice of religion is more extensive than even most Brothers think. I've encountered Brothers who stated that their jurisdiction requires monotheism. Given that there are entire jurisdictions in the world in countries whose majority religion arn't monotheist I've asked them to show the requirement. Only a tiny number of states have such wording so it tends to be an incorrect assumption on the part of any one Brother. I know of one state whose petition referred to monotheism 25 years ago but their petition now does not. It looks like they noticed that as a deviation from our principles of free choice and corrected the wording.
By the way, does anyone here know the back story on the GLofNY petition change? Back in the 1990s I downloaded a petition and it said something like one true and single living God. Now it says supreme being in line with most states I know about. Excellent change to line up with our landmarks in my opinion but I don't remember any discussion about it over the years.