This explains everything a lot better than I, or anyone else here can:
http://www.crucibleservice.com/eselector/general/generalpart1.html
It mainly talks about tool steels, but the ideas expressed here are universal for
all steels.
Just a few relevant paragraphs I randomly picked...
"Hardness is a measure of a steels resistance to deformation. Hardness in tool steels is most commonly measured using the Rockwell C test. Hardened cold work tool steels are generally about 58/64 HRC (hardness Rockwell C), depending on the grade. Most are typically about 60/62 HRC, although some are occasionally used up to about 66 HRC.
Toughness, as considered for tooling materials, is the relative resistance of a material to breakage, chipping, or cracking under impact or stress. Toughness may be thought of as the opposite of brittleness. Toughness testing is not as standardized as hardness testing. It may be difficult to correlate the results of different test methods. Common toughness tests include various impact tests and bend fracture tests.
Wear resistance is the ability of material to resist being abraded or eroded by contact with work material, other tools, or outside influences (scale, grit, etc.) Wear resistance is provided by both the hardness level and the chemistry of the tool. Wear tests are quite specific to the circumstances creating the wear and the application of the tool. Most wear tests involve creating a moving contact between the surface of a sample and some destructive medium. There are 2 basic types of wear damage in tools, abrasive and adhesive. Wear involving erosion or rounding of edges, as from scale or oxide, is called abrasive wear. Abrasive wear does not require high pressures. Abrasive wear testing may involve sand, sandpaper, or various slurries or powders. Wear from intimate contact between two relatively smooth surfaces, such as steel on steel, carbide on steel, etc., is called adhesive wear. Adhesive wear may involve actual tearing of the material at points of high pressure contact due to friction.
We often intuitively expect that a harder tool will resist wear better than a softer tool. However, different grades, used at the same hardness, provide varying wear resistance. For instance, O1, A2, D2, and M2 would be expected to show increasingly longer wear performance, even if all were used at 60 HRC. In fact, in some situations, lower hardness, high alloy grades may outwear higher hardness, lower alloy grades. Thus, factors other than hardness must contribute to wear properties.
[carbides]
Tool steels contain the element carbon, in levels from about 0.5% up to over 2%. The minimum level of about 0.5% is required to allow the steels to harden to the 60 HRC level during heat treating. The excess carbon above 0.5% plays little role in the hardening of the steels. Instead, it is intended to combine with other elements in the steel to form hard particles called carbides. Tool steels contain elements such as chromium, molybdenum, tungsten, and vanadium. These elements combine with the excess carbon to form chromium carbides, tungsten carbides, vanadium carbides, etc. These carbide particles are microscopic in size, and constitute from less than 5% to over 20% of the total volume of the microstructure of the steel. The actual hardness of individual carbide particles depends on their chemical composition. Chromium carbides are about 65/70 HRC, molybdenum and tungsten carbides are about 75 HRC, and vanadium carbides are 80/85 HRC.
These embedded carbide particles function like the cobblestones in a cobblestone street. They are harder than the steel matrix around them, and can help prevent the matrix from being worn away in service. The amount and type of carbide present in a particular grade of steel is largely responsible for differences in wear resistance. At similar hardnesses, steels with greater amounts of carbides or carbides of a higher hardness, will show better resistance to wear. This factor accounts for differences in wear resistance among, say, O1, A2, D2, and M4. Ideally, tool steels would contain as much carbide volume as needed for the desired wear performance. In fact solid carbide tooling is typically 85% or 90% tungsten carbide particles, in a matrix of 10% or 15% cobalt to hold them together. Chemically, the microscopic carbide particles in tool steels are similar to the carbide particles in solid carbide tools. However, very high amounts of carbide particles can lead to problems in grinding, or lower toughness. More comments on the effect of carbides on toughness and grindability are discussed in the following section: Effect of Steel Manufacturing on Properties.
Because of their high hardness, vanadium carbides are particularly beneficial for wear resistance. When present in significant amounts, vanadium carbides tend to dominate other types in affecting wear properties. For instance, M4 high speed steels chemical content is nearly identical to M2 high speed steel, except M4 contains 4% vanadium instead of 2%. Despite the high levels of molybdenum and tungsten carbides (about 6% tungsten, 5% molybdenum) in each grade, the small difference in vanadium content gives M4 nearly twice the wear life of M2 in many environments. In cold work tool steels, the carbide content in general, and to a limited extent the vanadium content in particular, may sometimes be used as a rough predictor of potential wear life.
Heat Treating Benefits of High Alloy Tool Steels
The heat treating process used to harden steels consists of heating them up to a high temperature (usually 1700/2200°F), then quenching to near room temperature, and finally reheating to some intermediate temperature for tempering (300/1100°F). A characteristic of low to medium alloy steels (A2, O1, D2) is that they soften from their maximum hardness somewhat during tempering. The amount of softening depends on the temperature exposure and the individual grade characteristics. To retain maximum hardness (over about 58 HRC), A2 and D2 are usually tempered around 400/500°F. Higher exposures result in lower hardness. A side benefit of high alloy content, typical of high speed steels, and most of the high wear resistance CPM steels, is that the tempering characteristics are changed because of the alloy content. They are tempered over 1000 F, yet retain their full hardness during this exposure."