This is a can of worms :-)
I am English, from the south; even within the British Isles there's some confusion as the names for root vegetables are regional, and that's why recipes vary so much.
However, I've discussed this before, and there's an authoritative description in Clarissa Dickson Wright's little Haggis book, so I think I can give an accurate answer.
First, if a British recipe says swede, it definitely means rutabaga, no question. A rutabaga being the dense orange fleshed root with a purplish skin.
When rutabaga were introduced to Britain from Scandinavia about 200 years ago they were, according to Clarissa D W, known as Swedish turnips.
in the south we soon shortened this to swede.
Further north they shortened this to turnip or yellow turnip.
In Scotland they shortened it all the way to neep; the neeps served with haggis are mashed rutabaga.
If I mention turnip I mean the small white fleshed things, usually with skin flushed either green or mauve, because I'm a southerner