Yes, it is nasty stuff. Whatever you call it.
One whiff in the lungs turns it to nictric acid.
I saw footage of the Shuttle landing at White Sands Missile Range (WSMR), They had a big fan on a truck that blew wind over Shuttle of a long time before they were allowed to exit the vehicle.
I lived in NM from 1972-1986, many of my Ham friends worked at the labs, military bases or NMSU.
Great bunch of engineers, electronic technicians and physicists.
The fuel part of that mixture is hydrazine and/or monomethylhydrazine and/or unsymmetrical dimethylhydrazine. “Aerozine 50” is a 1:1 mixture of (I forget which) two of those. Hydrazine generally will just kill you. Supposedly, if you smell it you’re already dead ... Or so they taught me in a range-safety briefing eons ago. The hangar had a hydrazine alarm: You hear it, you drop everything and GTFO.
Dinitrogen Tetroxide is the stuff that turns to nitric acid on contact with moisture. Like, as you noted, the lining of your lungs.
The mixture is “hypergolic”, which is to say that it ignites spontaneously on contact.
Both chemicals are liquid at reasonable temperatures, and are therefore very storable. That makes them good for reaction control systems, the small rocket engines used by spacecraft for orienting themselves. Shuttle burned a bunch of the stuff to orient itself for reentry, that’s why they had the big fans on it after landing. Even a little contamination is bad.
The stuff was used by both USA and USSR for ballistic missiles on account of it being storable. You could keep a fully fueled Titan ICBM in its silo for a long time, with no worry about either oxidizer or fuel boiling off. USSR used it in several systems, including the “Scud” IRBM and its derivatives, and IIRC at least one family of their submarine launched missiles.
Solid rockets are much safer to store and deploy ... ;’}