Strength: I believe the true definition of strength training is the kind of training powerlifters do, where they lift very heavy weights for very short sets (eg, 1-3 reps) and take very long rests (eg, 5 minutes). This promotes increased strength, but is not the most efficient way to increase muscle mass.
Hypertrophy: This is what bodybuilders do to increase muscle mass. They lift fairly heavy weights for sets of about 8-12 reps, and usually take about 1-2 minute rests betwen sets. This causes tears in the muscle fibers (hypertrophy), which then rebuild and grow to adapt to this kind of training. More muscle means increased metabolism. Some increase in endurance happens as well.
Endurance: This is where you lift lighter weights for long sets (eg sets of 15 upwards), usually with very short or no rests. This promotes increased endurance (the example Cathe uses is that you can hold your shopping bag for longer). In terms of what you actually "see", I'm still not sure about this one. I think the main benefit is that you become fitter in everyday life with this type of training.
In each case (strength, hypertrophy, endurance), you should lift the heaviest weight that you can safely handle for the particular rep range. So, although endurance workouts are termed "light", that doesn't make them easy!
Hope this helps,
Sharon.