So, the body has three main pathways that is utilizes to create energy. I will describe them in the course of one of my typical workouts. I'll use the workout I'm doing tomorrow.
Doing a leg triset workout will initially utilize the first energy pathway, which is the ATP/CP pathway. This just means the body is using the stores of Adenosine Triphosphate and Creatine Phosphate in your muscles. This lasts only for the first 5-10 seconds of the workout.
Next, as you continue doing barbell squats and deadlifts, your body will use the glycolytic pathway. This is when your body starts to create ATP from the glucose in your blood or the glycogen in your muscles. Lactic acid is the waste product of this chemical reaction. Eventually the acid is created to quickly to be flushed out the muscle, so you must slow down or stop (the rest between sets). It is then converted to the less toxic form lactate, which can also be used to make more glucose.
Because the leg workout does not take the full hour that you make available for workouts, you get on an elliptical. Now your body will utilize the aerobic oxidative pathway. Your body is now using the oxygen and glucose in your blood to make ATP.
It is only during the utilization of this pathway that your body will begin beta oxidation (fat burning). This chemical breakdown is one of the longest chemical reactions in the metabolism, so it is important to ensure you have enough carbohydrates to ensure your body does not turn on your own muscles as an energy source. As the intensity of the exercise increases, your body will use more carbohydrates, instead of fat. This is why low intensity, longer duration aerobic activities are recommended to optimize fat loss.
So ultimately, the morale of this story is that ATP is the source of movement. If you are a weight lifter, your muscles will hypertrophy to accomodate the stress that you put on it. This means the muscle fibers will grow larger, and one of those reasons is to store more ATP and CP at rest. If you are a runner, your body will become more efficient at utilizing oxygen to make ATP.
I try to lift weights and do enough cardio for fat loss. My muscles have grown quite a bit, and my run times have decreased. A good balanced fitness plan uses both anaerobic and aerobic means to get in and stay in shape!