[moocowduckquack]

Is pretty simple really.

Nothern Ireland is a part of the UK. So it definitely did not seceed from the UK.

The Republic of Ireland, is a seperate country with completely different government and currency, that used to be part of the UK but isn't any more, so it has definitely seceeded.

That county in Iowa, it is actually still part of the USA and has not managed to separate itself either legally, economically, or through force of arms. It is clearly not a separate sovereign nation. It has not seceeded from the USA.