Is there any difference between a rat and a skeever? As far as I can tell they llok the same and are about the same size.

Probably not. I'd say "Skeever" is just a Nordic slang term for a rat or something. Skeever is real world slang used to describe something repulsive, so it works pretty well for a giant rat.

Different breed, more acclimated to harsh Northern climates. Apparently they were smaller once, according to one innkeeper. It's unknown why they grew or if he was serious.