Ah, for some reason I thought you were referring to battered black pudding when you said you had different words :)

I'm not sure I'm familiar with sausage dinners. I think with all the supper/dinner terminology it ought to be a vague term to mean "a main meal involving fish/sausage/whatever" rather than something with a very specific meaning. I think I expected a fish supper to involve something other than just fish/chips (like a side dish or a sauce), though I wasn't sure what. Possibly it varies from shop to shop.