The IRA was a long-standing organization, going back generations, and in some respects centuries. It was entirely generated domestically.
Hizbollah was entirely organized by an external actor, to serve the interests of that foreign power. The “separate” political Party is simply diplomatic cover for their covert identity as an Iranian proxy. They have been agitating and propagandizing the Shia in Lebanon for the last several decades, as well as paying recruits and bribing the population, so they can now rally some votes using identity politics, Jew-bashing, peer pressure and secret police style intimidation.
Regardless of their “Political Party”, Hizbollah responds to the orders of Iran over the interests or preferences of their constituents, whenever their is a conflict. The political party is a mechanism to control public resources and the population, not to represent their wishes. It was very unpopular to sacrifice so many Lebanese for Iran in Syria, and put to lie much of the long term messaging of Hizbollah, as being dedicated to Lebanon’s defense against Israel.
European Governments recognize many terrorist front groups for the purposes of negotiations (and to pander to muslim voters domestically). It is just a useful fig leaf. The Palestinian Authority/PLO is another popular example.
Hezbollah political party members actually hold seats in Lebanon’s elected legislature, so they are clearly more than just a bunch of armed thugs.
The IRA had plenty of friends among the Irish trash right here in our own U.S. government over the years.