Most of us fitness buffs want all we can get of both. However, the training for each is different partly because muscle endurance/aerobic fitness is based on Type l muscle, and strength on Type ll - the power fibers.
High frequency, repetitive exertions train for endurance (eg jogging, biking, high-rep lighter weights, calisthenics), while heavy weights (things you can only do 4-8 times at most) train for strength.
Strength vs. Endurance Exercises