Here are the key differences that will come into play in negotiations between Britain and Sinn Fein, the IRA's political ally:
Britain says Northern Ireland, also known as Ulster, is a legitimate state that deserves to have its pro-British majority opinion respected. Key to that would be a reformed Parliament in Belfast, the capital, with Protestants and Catholics sharing power.
Sinn Fein says Northern Ireland is an illegitimate statelet to be subsumed within an all-Ireland state as part of any lasting peace settlement; Protestants in northeast Ireland would get written guarantees of equal treatment within a state governed principally from Dublin.
Britain has pledged that any agreement at round-table talks would be put to a referendum in Northern Ireland, which has a pro-British Protestant majority.
Sinn Fein says the referendum must be a single vote throughout Ireland, calculating that Northern Ireland's pro-British constituency would be outvoted.
Britain says its 18,000 soldiers in Northern Ireland will maintain patrols so long as the public needs that reassurance, and troops will be based there so long as Northern Ireland remains linked to Britain.
Sinn Fein wants the troops withdrawn quickly, not just from active duty alongside police but entirely from Northern Ireland.
Britain says the Royal Ulster Constabulary, the province's mostly Protestant police force, is a professional body that must be free to patrol. It wants more Catholic recruits and blames the IRA for preventing this.
Sinn Fein wants the RUC disbanded and IRA members given an official role in policing Catholic republican areas.
Britain says Sinn Fein must agree to disarm their movement in advance of entry into broader discussions, because other parties won't negotiate with a party keeping its guns and bombs figuratively "under the table."
Sinn Fein, noting its 12 percent share of the Northern Ireland vote, says this can happen only after broad talks with other parties. The IRA would hand over its weapons in conjunction with the withdrawal of British troops and Protestant police, the dismantling of British military installations, and the disarmament of Protestant "loyalist" paramilitary groups.