Seats like Stirling and Falkirk Burghs in Scotland were a legacy of the Act of Union and having to adapt the way that Scotland elected its MPs to the new British Parliament. Basically what they did was rather than have every Scottish Burgh electing an MP they were merged into fourteen District of Burghs seats which were non-contiguous with the other shire areas not in a Burgh elected a County MP (unless you lived in the six smallest counties which were seen to be too small to deserve to elect an MP in their own right so rather than merge them for Parliamentary purposes they made it so that they paired them up and have them elect MPs for alternate parliaments; with each being unrepresented half the time). Prior to the Great Reform Act these were... dodgy even considering the state of Parliamentary elections; the Burghs elected Commissioners who'd meet to decide who the MP for the District should be so it wasn't really a proper election. The Great Reform Act fixed a few things (direct elections for all MPs the main one) but the basic system of pairing small burghs together into a non-contiguous seat continued on in Scotland until 1950 with it spreading to Wales with the Caernarfon Boroughs seat (I think; could have the County wrong) which was basically the same thing as the Scottish seats. The 1885 and 1918 Reform Acts created more modern constituencies in some areas but the District of Burghs survived in lots of Scotland until 1950 with the Dunfermline Burghs and Kirkcaldy Burghs (abolished 1974) and the Stirling and Falkirk Burghs (abolished 1983) lasting a little longer.
Most Welsh counties had them. The odd thing about Caernarfon Boroughs is that it survived until 1950, whereas the other Welsh ones were abolished in 1885 or 1918. IIRC it has been suggested that it survived because of who its MP was.
As I understand it, the areas of boroughs were technically included in county constituencies as well, and that under some circumstances people who lived in the borough could vote in the county. So where I live now was, from 1885 to 1918, part of both the Hallam Division of the Borough of Sheffield and the Hallamshire Division of Yorkshire. This is obviously rather hard to show on a map.
(According to
Wikipedia, "The Municipal Borough of Sheffield was also a Parliamentary Borough and so the only electors from that area entitled to vote in Hallamshire were those who were freeholders. They could, of course, also exercise their vote in the appropriate division of the Parliamentary Borough of Sheffield. However, there were always considerable numbers of Sheffield freeholders who voted at elections for Hallamshire according to Henry Pelling in his Social Geography of British Elections 1885-1910.")
