The IRA campaign that began in the late 1960s was the latest round to reunite Ulster with the Republic of Ireland. It began with protests against Protestant discrimination against Catholics over jobs and housing in Ulster. It escalated into what would have been civil war if the UK government hadn't sent in troops to try to keep the peace. Many, including military, died on both sides

The latest IRA leaders were Marxists, as well as nationalists, and  took their campaign to the UK mainland, as in the past, to achieve their aims. Unlike Islamic terrorists, they had no wish to attack democracy and substitute a theocracy in the UK as part of a global caliphate. Their campaign was not against the British way of life but to effect a change in Ireland.

Many people in Britain either sympathised with the aims of the IRA or would have been happy to see to pull British troops out of NI. Not many people in the UK sympathise with the aims of IS.
That's the difference.