Annealing is softening the metal to work it. Typically, heat it to cherry red and let it cool slowly.

Tempering is toughening the metal after hardening. Once hardened (typically done by heating to non-magnetic / cherry red, then cooling quickly by quench), the steel is 'glass hard' and glass brittle. It will break easily.

To Temper, the hardened steel is heated to a moderate heat in order to essentially undo some of the hardening. Typically this is done either with a torch (by color) or in an oven set to the right temp for the steel, which varies

Jim