I'm thinking its what we always called a whiz wheel.  Properly called an abrasive cutoff disc. 

Interesting, "waver wheel" is what it is called where I worked here in NY.  Looked at the internet, seems the proper name is cut-off wheel.  We did use those two names interchangeably.  The type I used was like 1/16" thick, and 3-4" in diameter.  Sorry for the confusion.  

Drilling spot welds is a waste of time on floors. You are scrapping the old floor, so just grind through it where the spot welds exist. This eliminate having to fill a bunch of holes.
I grind them with a 40 grit floppy wheel until they ate thin, then use an sir chisel to separate the two pieces, then smooth off the spot weld with the floppy until it looks like an original piece of sheet metal.  You are going to scrap the top layer anyway, and you are going to have to smooth out the lower level, so just skip the step that leaves alot of holes.