Strength, hypertrophy, muscular endurance, power

Below is a graphic that illustrates the current state of knowledge concerning training for these various abilities.  Although this is presented as fixed categories, the reality is that this is a broad continuum.  There is a significant "bleed over" from one category to another.  However, these variables are often employed as shown below in designing periodized training programs that focus on a single fitness component for one training block at a time.  For example, a football conditioning program may focus on hypertrophy early in the off season, followed by a strength block, and finally a muscular power block right before the season.  In season may be a combination of muscular strength and muscular power.  This is classic linear periodization.  A non-linear periodized approach may combine several of these fitness components in a single week.  For example, Monday might have a hypertrophy focus, Wednesday a strength focus, and Friday a muscular power focus.  Non-linear periodization is more appropriate for athletes who do not have a fixed competitive season (i.e., tactical athletes).  Both linear and non-linear periodization can be effective. 

Note:  Core = primary lifts like squats or deadlifts.  Assistance = accessory lifts like curls or calf raises.  Power = explosive lifts like cleans or snatch.