You're talking about fast and slow twitch muscle fibres.
There are 3 distinct different types of muscle fibres. They Type 1, Type 2a, and Type 2b.
Every muscle in your body is composed of those different types of fibres, and the proportions with which they occur in your body are genetic.
Type 1 fibres are generally referred to as 'slow twitch'. They fire more slowly and are better at firing repeatedly without lactic acid buildup. They basically operate as endurance muscles and are oxidative in nature.
Type 1 fibres produce low levels of force, but can fire continuously for long periods of type. They are smaller in size than other muscle fibres, so somebody with a genetic majority of type 1 fibres will be quite slim. For a good example of type 1 muscles in action, look at maration runners. Their muscles don't need to produce a lot of force - only enough to put one leg in front of the other - but they are capable of producing that force for hours at a time. Marathon runners are not very muscular due to their predominance of the smaller type 1 fibres.
I'll skip now to Type 2b fibres (and discuss the importance of type 2a in a sec).
Type 2b fibres work the opposite way to type 1. They fire very quickly - producing greater force - but cause lactic acid to build up quickly. Subsequently they generally have low endurance, but are larger in size than type 1 fibres. Think of 100m sprinters: massive guys with huge muscles, capable of generating incredible force over short periods of time, but unable to sustain it. Type 2b fibres are anaerobic in nature and thus tire easily. They are used for short bursts of high force-output such as sprinting or weightlifting.
Type 2a fibres fall somewhere in between, and contain some characteristics from each of type 1 and type 2b fibres. They are anaerobic like type 2b, but are capable of producing force longer than type 2b. Recent research has shown that type 2a fibres can be recruited by the body and trained to function similarly to either type 1 or type 2b fibres as a response to repeated stimulus.
What does all this mean?
Your muscles are built from a mix of endurance and power muscles.
Your genetics will largely determine which of these types form the majority of your muscles. Ever seen a white guy in 100m Olympic final?
Endurance muscles are small. Power muscles are big.
Endurance muscles keep on keeping on. Power muscles fatigue very quickly.
You have some in-bewteen fibres (type 2a) which will respond to the training you are doing, and assist the muscle fibres you are stimulating. If you are running long distance, they will adapt to function like type 1 fibres. If you are powerlifting, they will adapt to function like type 2b fibres.
This is why, when we want to bulk up in the gym, we only use low repetitions. We want to stimulate the type 2b fibres (the bulky ones) in our body, not the type 1 (skinny fibres). If we were to do 12 or 15+ reps while lifting, we would start to recruit our type 1 muscles and develop them, which are of course smaller in nature. Thus we would not develop much in size.
PS I'm waiting for RawBlood to come and add some obscure information in an attempt to prove he knows more lol.