Sometimes stretching and weight lifting exercise are used interchangeably. However, stretches and exercises are completely different and serve vastly different purposes.
Stretching is the act of stretching a muscle, as the name implies. It's just like stretching a rubber band, you take the muscle from it's initial state and stretch to lengthen the muscle. This increases the degree of flexibility in that particular muscle. A minimal number of calories are expended due to the very low intensity of stretching.
Weight lifting exercise is quite the opposite of stretching. During a resistance training exercise, you take a muscle from it's rested state and contract, or shorten that muscle. Due to the degree of force required, it does expend a significant number of calories.
Weight lifting does decrease your flexibility, due to the continual contraction of muscle groups. Furthermore, following a relatively intense training workout, your muscles will undergo severe muscle trauma, resulting in muscle soreness and a reduction in your flexibility of the muscles that are subject to this microscopic damage.
Even though stretching and weight lifting exercise are quite different from each other, they compliment each other effectively. If you do lift weights regularly (and most people should for general health alone), then stretching is important to maintain a good degree of flexibility. The benefits of regular stretching are discussed in a previous post of mine, The Benefits of Stretching.
Let's consider an example of a stretches and weight lifting exercises that targets the same muscles, the calf, located between the knee and ankle on the back of your lower leg. I have chosen this particular muscle group because the stretch and corresponding weight lifting exercise is very similar in nature.
A common method to stretch your calf is to stand on a step with the front of your foot, and drop your heel down below the step height. You will feel a stretch behind your shin. This will enhance the flexibility through the calf.
Meanwhile, a common calf exercise is a standing calf raise, as shown in the diagram below:
You can see that the person begins in a stretch (as per the flexibility exercise described above), but then presses up onto his toes into a full contraction, where the calf muscles are shortened in this position. He then lowers his heels back into a stretch.
As you can see from this example, stretching is quite different to lifting weights.
Hopefully this has shed some light on this particular topic of the difference between stretches and weight lifting exercises.