"Hamas and Hezbollah were both resistance groups that either evolved or were created for the express purpose of removing a foreign occupying power. I do not understand how or why they differ from the IRA all that much. Can you explain why you differentiate them?"
First let me also differentiate between different IRA groups. I do not consider the 'Real IRA' nor the 'Continuity IRA' (though I believe they did recently lay down their arms) as representatives of the Irish Republican Army. I consider the 'Provisional IRA' the only true representatives of the Irish Republican Army. It is possible to argue in favor or the INLA and the Official IRA, but to defend them as well would be to time consuming and draw away from the general defense I am trying to provide.
Now, the differences between Hezbollah, Hamas, and the IRA in what would be their 'mission statements' is non-existent. However, the actions of kicking the Palestinians out of an area in which they live, while reprehensible, was extremely different than the situation in Northern Ireland. There are 800 years of history separating them, but I'll leave that out as it deals only with emotion, rather than the true problem.
First, and correct me if I am wrong (I am not a scholar of Israeli nor Palestinian history), I believe Palestinians were offered full Israeli citizenship. In Northern Ireland, Catholics were not able to own land (a hold over from the Penal Laws which were 'ended' in the mid 1800's. The actual practice in Ulster, though, was similar to the Jim Crow laws in the South of the United States. Though this is a problem to begin with, in Northern Ireland, you needed to be a landholder to vote. Therefore, the representation of the Catholic population in Ulster did not exist. Similarly, the police force in the North was made of up protestants.
This intense discrimination was first met with civil rights marches. These marches, though, were continuously attacked by Protestant groups and the Police force. Finally, these acts led to the Battle of the Bogside in Derry. This was BEFORE THE IRA had taken any actions. The British Army was deployed because the Protestant government realized it would likely be unable to hold onto power by themselves. This led to the resumption of activities by the IRA which eventually split (more technicalities, from here on I will refer only to the provos except where necessary).
Now, the reason I gave all this background history is to show the differences immediately proceeding the resumption of activities by the IRA compared to the actions by Hamas and Hezbollah. The difference being that Catholics in the North were denied of rights whereas Palestinians in Israel were removed from their houses (though often of their own volition I believe, and they came back to find that their houses had been repossessed by the Israeli government? correct?), and given the option to find new housing and become members of Israel. This was also after beginning a war in which they lost Palestinian land that had been given to them (in 1949?).
The second major difference is the actions that I am familiar with between the IRA and Hamas/Hezbollah. Now, I have studied IRA history and not Palestinian, so I only know of recent attacks by Hamas and Hezbollah. However, these attacks have indiscriminately targeted areas in Israel. Civilians have been targeted as much as (or more than) the military of Israel because these targets are simply easier. The IRA, though their targets and actions were brutally carried out, did target British military, Ulster paramilitary, and RUC policemen. Civilians were never a target (unless former military members), and often times warnings were called in by the IRA themselves.
This difference I believe is the main reason that the IRA must be separated from the other paramilitary groups. They carried out what can be described as 24/7 guerrilla warfare. However, they targeted only their enemies. They did not kill for shock value, but instead to inflict casualties on their enemies actual resources. Can you blame the IRA for being too brutal and taking the wrong approach? Of course. But, you must answer for Bloody Sunday and the absolute abysmal treatment of Catholics in the North if you do so. Malcolm X once professed that African-Americans must choose either the bullet or the ballot. If Malcolm X had been Irish, he would have only professed that the Catholics must choose either the bullet or the continuity of prejudice.