CONtinuity or DIS continuity?

The terms continuity and discontinuity are hard terms to grasp, at least for me.  Continuity is defined as an uninterrupted connection without any essential change. Not surprisingly, discontinuity refers to the lack thereof.  Typically speaking, continuity is a good thing.  If there is no continuity in speech or in an essay, there is a problem.  However, it seems that if there is discontinuity present within Islamic History, then this is actually good. Authors Sizgorich, McNeil, and Donner discuss Islamic history.  However, they each take a certain position on continuity vs. discontinuity of early Islamic history.  Ok, well what is the issue here?  The issue is relatively simple.  These sources open themselves to various interpretations regarding Islamic history.  How should we explain the history of Islam?
I like to think of Islamic history being discontinuous.  Well, for a while, things were continuous but at some point, I like to think that there was some initiation of change.  William McNeil discusses transportation in a historical perspective.  Thus, his historical  framework is broad and overarching.  McNeil discusses camels, which were extremely important for Arab culture.  Camels assisted in many everyday tasks.  These animals were truly a gift from God.  They were the “wheels.”  How else would Arabs trade and build civilization?  Who knows.  But, camels definitely were a significant part of Arab culture.  They excelled at long distance traveling.   Camels were not always used for long distance traveling though.  They were first used for milk purposes.  Thus, there was a period of change and discontinuity to propel Islamic culture.  Camels were now being used for something else-a different purpose was now being served.
Donner’s article From Believers to Muslims forces me to revisit the concept of continuity and discontinuity.  I agree that there was discontinuity within Islamic History, which change was necessary.  However, there are certain things that should be continuous.  The basic belief system-belief in one God, belief in the Day of Judgment, etc.  In this, continuity is imperative.  Donner also assumes a position of discontinuity.  “Believers” referred to this belief of the oneness of God including Christians, Jews, and monotheists.  But, a “believer” was different from a “Muslim,” or one who submits.  So there was a change as illustrated by the title of the article from “believer” to people actually referring to themselves as Muslims.  This was discontinuous.  It was different as people were now redefining themselves.
Finally, we have the position of Tom Sizgorich who “seeks to offer an alternative to the frequent tendency to treat Islam as discrete from the world that it took place.”  Thus meaning that Islam is continuous and no different from the world in which it unfolded.  This is interesting to think about.  There were significantly new things that occurred in Islamic history like the rise of the caliphal state.  But, perhaps this was not “that” new to Sizgorich.
It strikes me that there were aspects of continuity as well as discontinuity (if we mean change and no change) in Islamic history.  Again, the issue is the lack of information/documentation to successfully answer every question.  Instead, there is a range of interpretation.