That would be interesting to know...
English has pig (from the old term for a young pig- pigling), swine (Germanic- e.g. schwein = domestic pig; originally proto-indo-european 'su'), hog (related to 'hew', i.e. a castrated male pig), and boar (proto-Germanic, possibly proto-indo-european, meaning 'boar', but possibly in the sense of it being a terrible beast). Gris seems to come from gríss, which is Old Norse and has not been loaned to other Germanic languages.
None of that actually answers your question of course!
Native speaker here. I don't believe there is a difference in nuance between gris and svin when you're talking about the actual animal other than that gris is more common. When it's a person you're comparing to a pig though, "gris" gives me the impression that the person is dirty/sloppy/etc. ("Look at how she eats. She's such a pig!") while "svin" makes me think more of someone with a nasty personality ("You sexist pig!").