We all have thousands of different types of muscle fibers, but they can all be classified into 3 main categories. We have Type I slow twitch, and Type II fast twitch muscle fibers. The fast twitch can further be classified into type IIa, and type IIb. Each individual has a unique distribution of each type, and athletic performance is greatly influenced by the ratio of each type.
Type I slow twitch fibers simply put are endurance muscles. These muscle fibers are red in color and have an abundance of mitochondria in the cells which allow the muscle to use the aerobic energy pathways such as respiration more efficiently. This means that the muscle will have great endurance, fatiguing slowly. These muscles produce force at a slower rate than other types, but can still provide plenty of strength, such as the muscles of your abdominal and deep spine which are constantly being used. An example of a slow twitch dominant athlete is a distance runner, or triathlete.
The type II fast twitch fibers are explosive strength and power muscles. These fibers are pink to gray in color due to less mitochondrion in the cells, and less of a need for oxygen rich red blood to produce energy. These muscles produce energy and force very quickly, and use anaerobic energy pathways such as glycolysis, and the ATP-CP system. These muscles fatigue very quickly, but the force produced is highest. The energy pathways will provide energy in the absence of oxygen for up to 90 seconds. These are the muscles used in weight lifting, sprinting, and quick changes of direction. An example of a fast twitch dominant athlete is a professional football player, or soccer player.
You do not use these muscles separately. They are all being used all the time but in different ratios. Same goes for the energy pathways which power them. Knowing the difference between the fiber types, their strengths and weaknesses, and an idea of which you have more, then you can figure out how to train to your strengths.