Ulsan Station is not Ulsan Station. Or rather the station formerly known as Ulsan Station is now Taewhadong Station. Ulsan Station (which I doubt is even inside of Ulsan) is over in never-never land (near Tongdosa, best I can tell) being the new station for the recently opened KTX (high-speed train line). That fact was learned the hard way when R,A and I tried to get to the station formally known as Ulsan Station so they could go back to Busan and then I could continue on to the station currently known as Ulsan Station so I could take the KTX home.
Does your head hurt? Good. I know ours did. I ended up getting out at Taewhadong Station (the station formerly known as Ulsan Station) and took the slow ass train to DongDaeDong (or some other such place) where I transferred to the KTX to go the rest of the way to Daejeon.
In other words, if you are formally from Ulsan and are visiting, note the change in names of the stations so you end up where you want to go and not a 20000 taxi ride away from it.