“Ireland” is the geographical island. “Republic of Ireland” (officially Ireland) is the sovereign state covering ~80% of the island. Northern Ireland is the remaining part, belonging to the United Kingdom.
The Republic has its own government (parliamentary democracy), legal system (common law + Constitution), and flag (green-white-orange tricolour). Northern Ireland operates under UK jurisdiction with devolved powers. They are not two separate countries—rather, one island, two political jurisdictions.