Complicated.
England, Wales and Scotland are separate countries that share a monarch. Wales was actually conquered by England, but Scotland was merged in after Elizabeth I died and her cousin, James VI of Scotland, became James I of England and Scotland. Collectively, England, Scotland and Wales are Great Britain.
Ireland was conquered by England, then about a century ago successfully rebelled and regained its independence, except for the six northern counties that remain in British possession. Britain certainly regards Northern Ireland as a country like Scotland and Wales, but I suspect the Republic of Ireland sees it as a part of its territory. The Belfast Accords which settled "The Troubles" (a terrorist campaign, heroic independence struggle, or long-running civil war depending on who you talk to) provide for a one-time referendum for it to join the Republic of Ireland, which will probably happen in 20-30 years because the pro-republic side is mostly Catholic and typically have more children than the mostly Protestant pro-British side. Until then, though, Great Britain and Northern Ireland are collectively the United Kingdom of Great Britain and Northern Ireland (or UK for short).
Scotland, Wales and Northern Ireland have their own parliaments with some powers (relatively recent creations - younger than me), but subordinate to the parliament in Westminster. Arguably, they were carefully designed to be ineffective. England does not have its own parliament, but demographics being what they are the Westminster parliament is heavily dominated by English MPs. Scotland also has a supreme court (and in fact a partially distinct legal system), again subordinate to the English one. Wales has the same laws as England, and I think Northern Ireland does too although I should probably double check that.
It's basically a huge pile of historical accidents and at-the-time expedient compromises glued together by tradition. IMO, we should probably sit down and design something that reflects where we are now and takes lessons from other countries' systems, but I don't think there's any appetite for it.