Quenched refers to using a coolant to cool the hot metal rapidly.
Normalized refers to deliberately heating the metal above its critical temperature and allowing the metal to cool substantially below its critical temperature.
Quenching affects different grades of metals in different ways. It may harden the metal or it may soften other metals.
Normalization is a time consuming inexpensive way to modify the grain structure of ferrous metals. It may improve workability or toughness.
Google "stainless steel metalurgy-normalization" and see what you get.