BBC One is the first and principal television channel of the British Broadcasting Corporation in the United Kingdom, Isle of Man and Channel Islands. It was launched on 2 November 1936 as the BBC Television Service, and was the world's first regular television service with a high level of image resolution.
BBC Two is the second flagship television channel of the British Broadcasting Corporation in the United Kingdom, the Isle of Man and the Channel Islands. It covers a wide range of subject matter, but tends to broadcast more "highbrow" programmes than the more mainstream and popular BBC One.
BBC Four is a British free-to-air television channel operated by the British Broadcasting Corporation. It was launched on 2 March 2002, with a schedule running from 7:00 pm to 3:35 am.

BBC One Scotland is a British free-to-air television channel operated by BBC Scotland. It is the Scottish variation of the UK-wide BBC One. For almost all of the time the channel is referred to on screen as BBC One Scotland
BBC Scotland is a division of the BBC and the main public broadcaster in Scotland. ... BBC Scotland operates the regional variant of BBC One, the BBC Scotland channel, BBC Radio Scotland, as well as radio and television outlets, Radio nan GĂ idheal and BBC Alba, which broadcasts in the Scottish Gaelic language.

BBC One Wales is a television channel operated by BBC Cymru Wales. It is the Welsh variation of the UK-wide BBC One and is broadcast in Wales from Broadcasting House in Cardiff. Wikipedia

BBC Two Wales is the national variation of BBC Two for BBC Cymru Wales. It is broadcast to Wales from Broadcasting House in Cardiff. The channel can opt out from the main BBC Two schedule to show Welsh made programming, however this is used less frequently than in the past. Wikipedia