some vegetarians eat them because they're either a) stupid and think fish don't have feelings, b) hypocrites or c) "dietary veterinarians" who do it for the health benefits, not for animal rights reasons.
as to the OP, most fish are scaly but covered in a thin mucous layer, so the answer is both. cartilaginous fish (sharks, rays and jawless fish such as lampreys and hagfish) do not have scales the way the majority of fish do, but instead have skin covered in billions of tiny tooth-like protrusions, so they'd be more "sandpapery" with a thin mucous layer.
So remember, when you're feeling very small and insecure,
How amazingly unlikely is your birth,
And pray that there's intelligent life somewhere up in space,
'Cause there's bugger-all down here on Earth.
Loki/Grendel/Gail/Beowulf/Camilla/River/Bathory/Arwen/Lafayette/Deb/Jack Skellington (soon)