The answers to these questions are beyond what can be provided in this space here. Scholars have spent oceans of time analyzing them. The only hope I have is to give a small glimpse of what has been written in such breadth and depth.
Essentially, one can see three main branches or forms of Islam. The Sunni section of Islam is the largest percentage of the religion's devotees. They embrace a very traditionalist approach to orthodoxy and view the execution of the religion with an emphasis on Sharia, the moral and legal code guided by Islam. The Shi'ite form of Islam is a bit skeptical of the Sunni understanding, instead preaching that there are "chosen" ones who embody the true meaning of Islam. The emphasis on allegory and martyrdom is a significant part of the Sunni understanding of Islam. From the Sunni interpretation of Islam, the establishment of figures such as "Ayatollah" becomes part of the discourse. The Shi'ite form is in contrast to the Sufi form of Islam, which stresses an inner spiritual dimension to religious worship. For the Sufi, the true embrace of Islam takes place before or prior to the trappings of power and political control that emerged when Islam became an established religious orthodoxy.
The religion is complex. The three branches find common spiritual expression in Islam, but have distinct and separate differences with one another. This intricacy and complexity is difficult to convey to the general public and requires a commitment to deeper understanding and embrace of curiosity. There is an understanding required to see how the different branches of the religion help to give it its character and what the different forms actually mean in terms of defining "Islam." These values are the opposite of those who wish to portray Islam as a religion linked with terrorism and destruction. There are many in the world who find it easier to reduce the complexity of the religion to a soundbite or a simple formula where "Islam= Bad." The reduction of this complexity to "moderate vs. fundamentalism" is one such example. The religion cannot be reduced to such a binary distinction because it does not exist in the spiritual frame of reference. There are moderate Sunnis and some would argue that the Sufis are fundamentalist in their intense approach on individual, spiritual identity preceding anything else. It is here in which the various forms of Islam and seeking to understand them are divergent with the standard "moderate vs. fundamentalist" claims. This is because such modern claims deny the historical and spiritual intricacy that Islam offers.