The Palestinian residents of East Jerusalem are not citizens of Israel- they have the status of permanent resident. Because of this status, they have blue identity cards and are entitled to benefits such as national insurance, health insurance and unemployment allowances; they are also obligated to pay taxes. But, there are three major distinctions between a permanent resident and a citizen.

1. Permanent residents cannot vote in national elections or be elected to the Knesset

2. Permanent residents do not carry Israeli passports and can only leave Israel with transit visas or Jordanian passports, if they have them

3. The status of permanent resident of East Jerusalem is a conditional and can be revoked if the resident moves the center of his life out of Jerusalem for a period of seven years or more.

Permanent residents live under the constant threat of losing their status if they leave the boundaries of Israel for more than seven years and can no longer prove they have a "connection" to Jerusalem. Permanent residence, unlike citizenship, is transferred to the children of the residents only if certain conditions are met. Since the Knesset passed the “citizenship law”, it has been illegal for Jerusalem permanent residents to bring their spouses, who do not have permanent resident status, to live with them in Jerusalem. 

More information:

B'Tselem: Legal status of East Jerusalem and its residents Presentation by ACRI Attorney Sharon Abraham-Weiss to the ICJ Eminent Jurists Panel on Terrorism, Counter-Terrorism, and Human Rights