- 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, and also Ahmadiyya Muslims who believe that a 19th century man named Mirza Ghulam Ahmad was the messiah who was to come at the end of times (very similar to the prophesied Second Coming of Christ in Christianity). As with Mormons in Christianity, many mainstream Muslims don't consider Ahmadiyya Muslims to be "real" Muslims, but they consider themselves to be so and they use the Qu'ran and most of the Islamic laws.
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 .