Annealing and Stress Relief are terms used to describe heating a part to a certain temperature, holding it at that temperature, and then cooling the part at a relatively slow rate. Think of it this way: You’re stressed from a long day at work (the heat treat term is “work hardened”). You need to relieve the stress. Sitting in the easy chair and relaxing, that would be stress relief. But once you get up, there’s still the nagging pain in your back/leg/shoulder.
Annealing gets rid of a lot more stress than a simple stress relief, and in many cases actually causes a softening of the material. You could say its equivalent to soaking in the hot tub or spa for awhile, then having a nice massage. A lot more of the nagging pain is gone.
So, stress relief is a lower-temperature heat treating process that relieves some of the residual stresses, and cools the parts slowly so no new stresses are introduced. Annealing, on the other hand, is a higher temperature heat treating process that relieves a lot more stress and also softens the material.
All metals and steels can be stressed, which means that all can be stress relieved. Many also get too hard, usually through too much stress, and can be softened. Plastic is the latest material that we’re annealing to relieve molding stresses.
Here are a couple of pictures of parts being annealed or stress relieved: