Siff and Verkhoshansky discuss the different qualitative characteristics of strength, based on the different muscular actions (Isotonic, Isometric, auxotonic, Isokinetic, and quasi-isometric). Namely, they state that the basis for the production of all sporting movements involves explosive strength and strength-endurance. Explosive strength depends on the load the body has to overcome (external resistance) and the absolute strength that the athlete may possess.
However, explosive force also depends on starting-strength, which is the ability to quickly develop the greatest force possible at the initial moment of muscular tension. They mention that this is true with all loads, but especially lighter loads (i.e., 20-40% 1RM).
As the load becomes heavier (60-80%+ 1RM) acceleration-strength comes into play. Acceleration-strength is the ability to produce force as rapidly as possible once the contraction begins (immediately after, and alongside, starting-strength). This is important as the load gets heavier because the muscles in use must be able to overcome the inertia of the weight and quickly produce the maximum strength possible, or the weight will not move at the necessary velocity.
Excuse me for being biased, but a very easy example would be a snatch or clean, where the weightlifter must possess the strength necessary to overcome the barbell's inertia (starting-strength), but must also be able to accelerate the bar quickly with that strength (acceleration-strength) to get underneath.
Siff and Verkhoshansky also go on to say that "the working effect of a sporting movement, executed with maximum voluntary muscle tension, is determined to a greater or lesser degree by the four special strength abilities: absolute strength, starting strength, acceleration strength, and absolute speed of muscular contraction" (p.127).
These abilities are independent of each other and are developed along different timelines, so to speak. They do not have direct effects on each other, and the greater one ability is developed, the less impact it will have on another. If your training revolves around explosive, lighter movements, than your ability to express tension/strength quickly (starting strength, acceleration strength) will be more developed than absolute strength. The opposite would be true if your training was based more on slower, heavier movements (i.e., your absolute strength would be more developed).
The abilities become more independent of each other as the athlete/exerciser's fitness level increases. This is obvious if you look at high-level athletes at the Olympic level, where the athletes are highly specialized. Therefore, a sprinter would not be readily suited to express strength characteristics that are not related to sprinting. This is where the general term 'specificity' comes into play. Also, the differing abilities require different amounts of training, as acceleration strength and absolute strength are "easier to perfect" than absolute speed and starting strength (p. 129).
This is just my take on what I have read at this point. You can take these comments with a grain of salt if you choose, but I believe this to be a good understanding of what Siff and Verkhoshansky originally meant. I will definitely look at the development and expression of strength in a whole new light now that I have this information available to me. Strength is not just one encompassing term as I had thought; it is a multitude of functional characteristics that can, and should, be trained differently/specifically.
I hope this shed some new light on strength development for you too! Train hard, train smart!
Siff, M. & Verkhoshansky, Y. Supertraining (4th ed.). 1999.