What is the difference between tempering and hardening metals and their end products?
As the names imply, hardening makes the metal more rigid but more brittle, and tempering (from "temperate", moderate), forgoes some hardness for increased toughness. Iron alloys are hardened by rapid quenching and toughened by annealing, but some copper alloys are made more ductile by quenching and are hardened by working.

In brief, annealing allows atoms to migrate to a less-strained position, whereas quenching lock atoms in place; this is used to make tempered glass, as well as to harden metals.

Extremely rapid quenching can produce a metallic glass, where precipitation of constituents is prevented.

Edged-tools may need the body to be ductile, so that it does not shatter, but require for the edge to be hardened so that it retains sharpness. See http://www.smt.sandvik.com/en/products/strip-steel/strip-products/knife-steel/hardening-guide/purpose-of-hardening-and-tempering/ or http://www.stormthecastle.com/blacksmithing/blacksmithing-a-knife/stock-removal-method-of-knifemaking-part-4.htm.