United Kingdom of Great Britain and Northern Ireland as it has been known since 1922 has a complex history. It's not technically a country but a nation state.

It's composed of two countries, Scotland and England. They were joined under the act of the Union of 1707 signed by both parliaments.

Wales was often referred to as a principality as it was incorporated into England way back in 1301. England and Wales make up the original United Kingdom.

So Wales joined the 1707 Union under the authority of England, although it retained Welsh culture and language and in recent years, especially it has come to be recognised as a country, perhaps more so since 2011 when it's got it's own devolved government

Northern Ireland is region, though it has its own devolved assembly. It's the bit Britain kept hold of following Irish independence in 1922.

After a nearly three century hiatus the Scottish parliament reconvened in 1999 following devolution.

I'm talking a lot about devolution that's basically how it sounds. Unions evolved in different ways at different times and then devolved back again.

England doesn't have its own parliament. Why? There's no need for one as it makes up around 83% of the UK parliament. Perhaps one day it will.

America celebrates it's independence day July the 4th each year. In 1776. The United States of America emerged from british colonies. They've never been countries as far as I know but I may be wrong about that.

TL:DR Being a country isn't a matter of self identification, but perhaps you may identify more strongly as being a citizen of a particular state over being an American. If enough people felt that way perhaps an American state can become independent and be a country but it's likely to be a long and difficult road because power is never given up lightly and you've not had the historical precedent.