I agree with Olandew. I also am not an expert, but just doing what I've been told is important by trainers, and I think my physical therapist. One phrase is "A long muscle is a strong muscle." This means working out tightens the muscle fibers and stretching the muscles out does just what Olandew says. I like stretching. I also have heard stretching during your workout any time you wish is also good.
I was told that too much stretching before working out could injure your muscles, to do a 5 minute warm up on cardio followed by two 8 second stretches for the muscles I am going to work out rather than a longer full stretches. The full stretches can be done as your muscles are worked out and particularly after the work out.
Today I stretch before and after my workout. I had back problems, and my physical therapist said it was good I stretch before and after. They are regular stretches you see a lot of people doing. I go easy before I work out. If I am working out my chest, I only do a couple of short stretches for my chest (and triceps) before I work out. That is after I do my routine stretches, and a cardio warmup.
After my workout, I do longer stretches of my chest and triceps, any other muscles. I follow with my regular stretches again, slowly at my own pace, stretching carefully and as much as I can. It feels good and is relaxing. I can tell it helps my muscles and flexibility.
I don't know about non-strenuous stretches after workout. Your muscles have been worked and are ready to be stretched out and need it. They are not cold muscles. I think how you stretch is what makes a difference. I work up to it. After my work out, I do three reps of each stretch. The first is a gentle warm up. I don't push much farther than my muscle wants to stretch. I find my muscles stretch farther in the second rep, so I push farther. The third rep of stretching the same muscle, I stretch as far as I can go comfortably.