The individual conflicts in the Middle East can be incredibly confusing as they all seem to stem from similar problems, but started for very different reasons. The other problem in understanding these situations are the separate groups involved and their classification by other nations as wither political parties or terrorist groups. A prime example of this are Hamas and Hezbollah who appear to stand for the same thing, but share little in common in other areas.
Hamas, meaning Islamic Resistance Movement, was founded in 1987 by Sheikh Ahmed Yassin and Mahmoud Zahar. It is a Palestinian political movement which is seen as a terrorist group by several countries due to the actions of its militant wing Izz ad-Din al-Qassam. Hezbollah, meaning Party of God, first came to prominence in 1983 after Israel invaded Lebanon. It also has a paramilitary wing which has seen many countries classify it as a terrorist movement.
Although both groups stand opposed to the Jewish presence in Israel, they are supported by opposing Islamic ideologies. Hamas are Sunni Muslims whereas Hezbollah are Shia. This is not a conscious decision. Palestine is overwhelmingly Sunni and Shia are the majority in Lebanon.
Although both Hamas and Hezbollah are political movements, they only really have one political view: the removal of Israel. The main reason for this is both parties were formed when their respective countries were invaded by Israel in the 1980s.
The international community has mixed views of both Hamas and Hezbollah. The United States, Canada and various other nations classify both as terrorist organizations rather than political parties. There are other countries, especially in the Arab world, who actively support both groups.