Catabolism refers to the body breaking down ANY of its components for energy, simply the opposite of "anabolism"; the process of building.
At rest and during light exercise, your body will use fat as the primary fuel. During heavy anaerbic exercise, however, the body will burn glycogen primarily.
When under stress, the body will do its damndest to meet whatever challenges its being given. This means it will burn fat, glycogen, or even your muscles, to keep activity going. This is simply how the body works; the biology of it is a bit more complex (let me know, and I can give some links or a longer explanation)
The exact percentages of fat vs. muscle vs. glycogen burned at any given time depends on SO many factors, but basically, after your workout, when glycogen is depleted and your muscles are damaged (stress-induced microtrauma), the first thing you want to do is give your body some fuel to repair and restock.
The way I see it, make your workout the time to force adaptation. Forget about the "fat burning zone" and all that other *expletive deleted*; go to the gym for your health and for your strength. Do cardio for the good of your circulatory and resporatory system, and lift to build (or maintain) muscle mass. Use your diet to gain or lose weight.