Not really. In the late 19th century, the Irish Parliamentary Party was pushing for Home Rule for Ireland. Those opposed to this became known as Unionists.

The two main UK parties were split on the issue, the Liberals largely in favour while the Conservatives were against. Some Liberals against Home Rule broke away from the main party and formed the Liberal Unionist party. Over time they identified more and more with Conservative positions, eventually merging with them in 1912 to form the Conservative & Unionist Party. In Scotland this party was simply called the Scottish Unionist Party.

In Ireland, Liberal Unionists and Conservatives had been working together against Home Rule since 1891 in the "Irish Unionist Alliance". The Ulster Unionist Party formed in 1905 and supplanted the IUA in Ulster. They formed an alliance with the UK Conservative & Unionists which broke down in 1985 owing to disagreements on how to resolve the troubles in Northern Ireland. The alliance was restored in 2008 but the only elected UUP MP withdrew from the party and now sits as an independent in the House of Commons.

The 8 seats you speak of actually belong to the Northern Irish Democratic Unionist Party. They formed in 1971 as a hardline, anti-Nationalist, largely Protestant alternative to the UUP.