Sport Specific Training
Sport performance is highly sport specific. Likewise, optimal training for sport performance should be highly sport specific.
Years ago, I demonstrated this concept by accident. At the time, I was road biking extensively. I trained 6 to 10 hours a week using a formal plan with periodization. I trained with a heart rate monitor. You would have thought my quadriceps muscles were highly trained. I found out they were trained for cycling not running. One of my bicycle wheels broke. It was in the shop for two days. On one of those days, I ran for 60 minutes which I thought would be a low intensity workout for me considering how much cycling I had been doing. The next two days I had very sore quadriceps muscles. This demonstrated that the low impact cycling work of my thighs was different than the high impact, plyometric work of running.
Boiled down to the simplest form, if you want to perform well in the sport of long-distance cross-country skiing, you should train by doing a lot of long-distance cross-country skiing, not by mostly running on a treadmill. That is not to say that running would not help you, but rather, long distance cross country would help you more. If you want to perform well hiking up mountains, do a lot of walking uphill rather than using an elliptical trainer.
This advice should not be interpreted as meaning that to train for a specific sport, you should only do that specific activity. For endurance sports, your aerobic, endurance training should mostly be in the specific sport. Cross training can be useful to stave off boredom and to help with recovery from sport specific training.
Almost all athletes benefit from some form of strength training. A base of general strength training is needed for almost every sport. On the other hand, if you are training for bicycle stage racing, your strength training would include a lot of hip and knee extension exercises as well as torso/core muscle training. You would not spend much time, perhaps none, aimed at building strength and adding bulk to your upper extremity muscles.
An excellent example of a sport specific training plan can be found in Training for the New Alpinism: A Manual for the Climber as Athlete. by Steve House and Scott Johnston. It is a sport specific training manual for alpine style mountaineering.