Is the word ulv a synonym for värg?
or does it apply to a different kind of animal?
Not quite- 'were' comes from the Old English 'wer', meaning 'male human'. 'Wearg' and 'wearh' both mean 'wolf'.
'Were' is pronounced something like Modern English 'wear a', whereas the other two are closer to 'warch'. (the 'ch' is pronounced like a German 'ch') and Swedish 'varg' (with a 'w' instead of a 'v').
Just adding for fun that the word värld/"world" is actually a cognate as well - it's comprised of verr and old, meaning "man" and "age"/"growing"/"happening", respectively. The world ålder comes from the latter part, so essentially, a world is a human epoch.
And an older Swedish word for brother-in-law was värbror. :)
I was studying both Old English and Old Norse before I picked up Swedish last year.
You'll find that the further back you go, the closer all of the Germanic languages become. For a long time, Old English and Old Norse were mutually intelligible with a little work.
As I can't sleep I will elaborate a little. 'Ulv' is the original word. People started using 'varg' instead because they were afraid to say 'ulv' out loud. 'Varg' was originally a word for the lowliest kind of murderer. One who kills people in the dark or by strangling, poisoning or other "dishonest" methods. This was 1000 years ago or so. Today 'varg' only means 'wolf'.
Still sometimes used, in the saying En ulv i fårakläder - A wolf in sheep's clothing, as the "wolf" part in werewolf - varulv and in the first name Ulf, so even if we'd pretty much never refer to an actual wolf as ulv, it doesn't hurt knowing it. Norwegians and Danes still use "ulv" as the common name for wolf as well.