Let's say you have a soap recipe that needs (picking numbers out of the air) 120 grams of NaOH to exactly saponify 450 grams of fat. When you make this recipe, there is no excess fat and there is no excess lye.
Strictly speaking -- To superfat the soap, you'd use the same 120 grams of NaOH, but you'd use more fat than 450 grams -- maybe 475 grams. The extra 25 grams of super (additional) fat will not saponify.
To do a lye discount, you'd use the original 450 grams of fat, but you'd use less NaOH, maybe 115 grams, instead of the full 120 grams. Again, using less lye means there is some fat left over that won't be saponified.
You
add fat in the superfatting method and you
take away lye in the lye discount method. The batch size increases when using the superfatting method -- the fat weight increases. The batch size decreases with the lye discount method -- the lye weight is reduced.
The unsaponified fat, regardless of the mathematical gyrations used, becomes the superfat in the finished soap.
Now that I've defined the strict definitions of these concepts, I have to say most people most of the time talk about superfat and lye discount if they are totally interchangeable. The soap recipe calcs do likewise. Most of us and most of the calcs are doing a lye discount calculation, but we aren't too strict on the terminology -- we might call it a lye discount or we might call it a superfat.
A lot of bath soap recipes nowadays seem to be superfatted from 2% to 8%, more or less. When I first started soaping in 2012, I seem to recall many people used somewhat higher superfats -- maybe closer to 5%-10%. There are hot trends in soap making just like anywhere else.
There are some soaps that are exceptions to this 2-8% superfat range. Probably the best known exception is the 100% coconut oil soap. If used for bathing, most people superfat this soap in the 15% to 20% range.
I have some more info here:
https://classicbells.com/soap/superfat.asp