Much of this information has been provided by Howard Clark of Morgan Valley Forge ; a consummate metallurgist and smith. All of this information is presented "as is".
Steel: Iron which is purified and to which carbon has been added.
Ferrite: Pure iron, body centered cubic crystal at ordinary temperatures.
Cementite: Fe3C, iron carbide. This is the normal structure of iron and carbon when steel is in an annealed state.
Pearlite: The lammelar structure that results from slow cooling from a high temperature. It consists of alternating plates of ferrite and cementite. The spacing of the plates, or relative fineness is determined by the temperature at which it was formed, as is the hardness.
Austenite: The solid solution of carbon in iron. In low alloy steels it can normally only exist at elevated temeratures. The molecular structure is a face centered cubic crystal, allowing lots of room for carbon atoms. Austenite by definition does not require any carbon present. It is what you have when the shift from body centered cubic to face centered cubic structure of the crystal lattice occurs, with or without carbon.
Martensite: The usual condition that is referred to as hardened steel. It is the result of rapid cooling of austenite, trapping the carbon atoms inside the face centered cubic structure. This causes the cubic structure to distort into a tetragonal shape that is highly stressed, and thus quite hard.
Annealing: Softening the material so that it can be easily fabricated/machined. There are a number of methods and structures that can be described as annealed.
Full Anneal: Steel is heated to a temperature above the austenitic phase transformation temperature (also called A1 or CRITICAL) and held at this temperature long enough to allow the mass to convert to austenite then cooled very slowly to produce a coarse pearlite structure.
Spheroidized Anneal: This consists of a ferrite matrix with all the carbon as relatively large size spheroidal carbides distributed evenly throughout the ferrite matrix.
Normalizing: Softening the material so that it can be easily fabricated/machined. This is similar to a Full Anneal but after the steel is converted to austenite it is allowed to cool to ambient at a more rapid rate. The normalizing process is most frequently used to relieve stresses in a piece of stock prior to hardening. This lessens the occurrence of stress failure between the hardening and tempering processes.
Hardening: Heating the workpiece to a temperature above the austenitic phase transformation temperature (also called A1 or CRITICAL) to make austenite, then cooling rapidly to produce martensite.
Tempering: Re-heating the as quenched martensite to a lower temperature to relieve some of the stress. This lowers the hardness some, but greatly increases the toughness.