Annealing involves temperatures of 1200F and above. Traditional “full” annealing is above the upper critical which is even hotter and involves recrystallization of the steel, so it bears very little resemblance to tempering. Spheroidal annealing is below the lower critical temperature (1200F-1333F) and here the lines gets blurred a bit with tempering but the desired outcome is still very different. The purpose of annealing is to soften the steel for cold working operations and machining, and the goal is as soft as possible. This is accomplished by taking as much carbon as possible out of solution and segregating it into coarse carbide and to remove any work hardening effects by recrystallization.
Tempering involves temperatures from 300F to around 800F, but most knife applications are a range from 350F – 550F in simple carbon steels. The idea here is not to soften the steel but to toughen it instead so that you maintain hardness without brittleness. Quenched steel is not only hard it is strained by super saturation of carbon in the iron, tempering relieves some of the stress by letting very small amounts of carbon to come out of solution in a very slow and controlled process. Annealed steel will lose 30 points Rockwell or more, but tempered steel will only loose from 2 to 7 points.