Specific, neuro-muscular movement patterns are the most important factor in exercise training adaptation. The cardio-respiratory system's capacity does improve. But, it improves in context of the specific neuro-muscular movements. Unfortunately, the lay public will simply view it all as just 'cardio', failing to appreciate the important differences in movement patterns.
While all of this can get complex, I like to distill this complex physiology into a simple and applicable theory.
The Movement Force-Rate-Duration Theory
The specific neuromuscular pattern of any movement has three, interrelated performance components: force output, the rate that the force is developed, and the duration that the force and rate of force development needs to be maintained. Here is a diagram showing the relationship of the three components.
For a given movement, all of these components are required at a minimum level. Our genetics determine partly the development of these components, hence why people gravitate toward a given sport or exercise. Additionally, if we have a deficit in one of these components, it needs to be developed with proper training.
Lets apply the Movement Force-Rate-Duration Theory to running a 5K race. A low-moderate level of force needs to be developed at a modest rate and at a moderately long duration (for the average person). If we determine which component is the weakest, we can focus on improving it. If force development is weak, then slow strength training with adequate resistance will help. If the rate of force development is poor, then training to develop force development with explosive strength training (and moderate resistances) or plyometrics will help. If the ability to maintain the force or rate (endurance) is poor, then that needs to be trained as close to the same neuromuscular pattern as possible by running in the same environment (surface, incline, altitude, temperature, etc.).
Another example of how to apply The Movement Force-Rate-Duration Theory is 'cardio' for golf. A client of mine, who is an avid golfer, has been using an elliptical trainer and spin cycle many days per week in addition to his golf. I changed his 'cardio' to uphill walking, kettlebell swings, rotary medicine ball throws, and lateral low-box hopping. The walking is a basic movement on the course, and the ability of the hips to withstand fatigue in extension and rotation movement patterns are also very important. These movement patterns are closer to the what he will be doing over the duration of three hours on the golf course than the elliptical or spin cycle.
Conventional categorization of exercise into 'cardio' or strength training is not only misleading, but a disservice to trainees. Adaptation to any exercise training is neuro-muscular pattern-dependent. It is not a choice between using your muscles or your heart. It is a question of what movements do you want to improve. Once you have developed foundamental movement patterns (mobility, stability, coordination,etc.), applying the Movement Force-Rate-Duration Theory to your training will help you address the three performance components of physical movements (force, rate, duration) and will help you achieve superior results.