- There are no types of muslim
- Muslim is the one who believe on the oneness of Allah
There is NO God except Allah
And Mohammad is His messenger
'(may peace & blessings be upon him)'
There are in fact many different . However, they all believe in the same God and believe in almost all the same laws and teachings. It's very similar to the different denominations of Christianity.
The major sects of Islam are the Sunnis and Shiites, which can be roughly compared to Catholic and Protestant churches in Christianity. Sunni and Shiia use the same Qu'ran but have some different beliefs about the teachings of Mohammed and later philosophers outside of the Qu'ran, and their major split is over how leadership of Islam should be determined. So they're really very similar--they use the same Qu'ran and have almost all the same sensibilities, but as with , they consider their comparatively small differences to be extremely important.
Again, as with Christianity, there are also small sects that vary quite a lot from "mainstream Islam." There's Sufism, for example, which is an especially mystical branch with some unique outlooks on the laws of Islam, Ahmadiyya, Qadianis and Marzais, who claims that they are Muslims and believe in a 19th century man named Mirza Ghulam Ahmad as the messiah and new prophet are non-Muslims and out of the bounds of Islam. The goverment of Pakistan and many other Muslim nations have declared them non-Muslims. Ahmedis also consider the mainstream Muslims as non-Muslims. They believe in Mirza Ghulam Ahmed as the Bahais believe in Bahaullah as their prophet. But there is a difference between the two. Bahais consider themselves as the followers of a different religion, but the Ahmedis want to occupy the seat and name of Islam despite following a different person and different holy scripture.
Another important distinction you referenced was the difference between "peaceful" and "non-peaceful" Muslims. These are, for the most part, not different sects or denominations--they're just radical people within a given denomination. To cite another example in Christianity, Ireland used to have sectarian bombings and killings between Protestants and Catholics. These were never endorsed by either Protestant or Catholic leaders outside of Ireland, but there were self-proclaimed "leaders" and even clergy members int he country that advocated and assisted in these killings, which were basically a war over Protestant vs. Catholic control of .
^The top wasn't tripe. There are different sects of Islam, but because so many of these sects have been fighting each other and killing each other recently in the middle east, many Muslims are now trying not to label themselves as any particular sect, so as to promote unity among Muslims.