I'm born and brought up in the midlands, so the yellow-fleshed purple-skinned hard-fleshed one is a swede and the white-fleshed one is a turnip.
Years ago I had a boyfriend from Orkney then Durham, he called the yellow-fleshed purple-skinned hard-fleshed ones 'neeps'.
I now live in the far north of england where they are all called turnips. We just sowed some for fodder, and the (south eastern) seed merchant calls them fodder beet!
I love the yellow-fleshed purple-skinned hard-fleshed ones steamed (best along with carrot and beetroot too), grated (with carrot & beetroot is good!) raw, just raw to munch on, roast (I just brush with oil & lemon, but the syrup does sound nice), mashed with carrot, in stews - I think I wouldn't have it in a sandwich but other than that I think it's pretty versatile!
The white-fleshed ones to me taste fresh bright and oniony and I love them in pretty much all the same ways except they seem to gain a bitterness if they are roasted. I like the subtle fresh onion-ness so much I think that raw and steamed are probably my favourite ways to eat these ones. I use them in soups, stocks and stews for a delicate onion flavour.