The nickname of piss elm is a derogatory term that seems to get placed on just about any type of elm, depending on region or local custom. Around here it is often applied to young, small diameter elm that have lots of water in them when cut. I here the term piss elm quite often in the spring/early summer when the ground is wet and the trees are "waking-up" from winter sleep. The thing is that as summer, and dryer weather progresses those same trees won't have near the water in them and the term will die-out until the next spring. Sometimes those young, wet trees will have an odor (described as cat pee) which seems to support the nickname... although, I personally have never thought it smelled like cat urine, and never use the nickname because it does nothing to identify the elm species.
There is one elm that grows in the south, east of Texas, that (from what I've read) has a strong urine-like odor that can be smelled even without cutting... a position down wind from a stand can be a bit offensive. It is the Winged Elm (or Wahoo), a small tree considered a nuisance in many areas because it will "pop-up" in cleared areas and is difficult to get rid of. It is believed that this is the "original" piss elm... and that makes the most sense. Actually we have a few Winged Elm in extreme southeast Iowa along the Mississippi... I've seen it a couple of times but never noticed any odor (that I remember). A strange looking tree that has funky "wing-like" things growing on it... almost resembling some sort of mushroom or fungus.