They do have differences of opinion on a lot of central beliefs besides the historical reasons.
Besides the Sunnis and Shias, there are Ibadis (Oman), Druze (Lebanon, Israel, Syria), Allawis (Syria), Ahmadiyyas (Pakistan mainly) and Bahai'is (Iran, India etc.)
Sunnis are divided into 4 groups based on interpretation (Hanafi etc.) -- not much difference but the Wahabbis and the Sufis are sub-groups that display quite divergent paths
Shias are divided into 12evrs, 7evers and I believer 5 evers depending on the number of Imams they hold as being "true". They are Ismailis, Bohris, Dawoodi Bohras, etc.
I decided to look into the charges that the Libyan east is Al Qaida. I found that the overthrown King Idris (by Qadaffi 40 years ago) was Sannusi Sufi. Previous rulers in this line were very pious, and rejected the more athletic manifestations of Sufi. These rulers also managed to resolve disputes in surrounding areas and get along with other tribes as they were fairly relaxed in their interpretations of Islam so far as forcing others to toe the line. Thus it sounds as though they might not appreciate the extreme rigidity of Al Qaida.