Jennifer, I appreciate your expertise and clarification of your posts.
However, I wanted to respond on a few things to (I guess) clarify as best that I can one last time given you asked me to define strength.
Strength is defined as the potential tension a muscle is capable of applying in a single maximum contraction. Training for strength causes several physiological changes in muscle tissue. Of these, the two most important are improved nervous control of muscle and increase muscle size.
To compensate for the wide variety of possible load conditions (playing the piano does not require the same output as lifting weights), the CNS stimulates exactly the amount if fibers necessary to perform the job. If a muscle is just strong enough to cover the load, essentially all its fibers must contract and as soon as these tire, the muscle fails and cannot work again until there has been sufficient recovery.
However….if the muscle’s level of strength surpasses the job’s requirements, the CNS will only stimulate a portion of the muscle’s fibers, leaving those remaining in reserve, ready to take over when the initial bunch tires and ultimately fail.
It is this sort of alternation that increases your muscular endurance. Strength training specifically increases the muscle’s capacity to stimulate muscle fibers and hence endurance.
So lets look at your analogy. On one side we have a sprinter, who does explosive, high force movements and can exert himself maximally for only a short period of time. Lets now add some endurance training to his regimen. He adds 20% of his training time to running ½ marathons. After two months, he is now a slower sprinter, weaker, and physically smaller (more on that in a minute).
On the other side we have a high level marathoner. This person trains solely for endurance (as you prescribe). He does high levels of repetitive activity for his legs, increasing the number of mitochondria per muscle cell, substantially increasing his endurance. Lets now add some strength training to his regimen. He adds 20% of his training time to strength training with weight loads in the 65 to 90% of one repetition range. After two months, he can run farther, longer, and faster. Why?
Regarding training to fatigue / failure when strength training. This really is not necessary and will be detrimental in the long run. Powerlifters never train to fatigue and they are the strongest individuals on the planet. Olympic lifters also don’t train to fatigue and they are unbelievably strong. You only have to train within a range of load to get stronger and push for continual progression of load over time. Overload is key; not pushing the muscle to fatigue as it drowns in lactic acid after burning through glycogen, ATP, and CP. Consider that sprinters on the track don't train by running to fatigue where they fall down in a heap of vibrating mass (would be funny to see, however). They train at high intensity but it is something less than all out fatigue.
You mention the cross section of a muscle – yes, that is a byproduct of strength. Clearly increased fiber size does affect the physical appearance of the muscle but the degree to which it contributes is largely determined by diet.
Yup - made a boo boo on the cardio comment but I was really referring to metabolic conditioning and trying to see some 'abs' before summer rather than training to increase my endurance....I squat and deadlift for that (hee, hee). And yes, training for overall endurance does tap into the cardiovascular system. But you can actually have a muscle with high endurance without affecting your cardiovascular system. Consider a muscle with predominently slow twitch musculature. That muscle will be very enduring even though you are a 'couch potato'. The calf muscle comes to mind.
Anyhoo, I am done here. Need to go train.