Always wondered that too

Sort of. Yoga tends to incorporate isometric exercise with flexibility as well as some body weight strength building. Think of it this way: a champion sprinter, Weight lifter, and marathon cyclist all need muscle. The marathoner isn’t going to by default be good in the sprint and the sprinter has strong legs but isn’t likely going to beat the weight lifter at lifting with their legs.

But there is another type of strength. Being able to pick up 50lb sword isn’t the same as being able to swing a sword all day, and neither is the same as being able to swing a sword so fast it can’t be seen. But none of those allow you to take a 5lb sword and hold it out parallel to the ground for 10 minutes without shaking or lowering it.

Tl:dr- yoga helps stretch some but it also helps with range of motion. Many yoga poses require you to lift or lower your own body weight- which builds strength. Yoga also requires you to support your body weight or the weight of limbs for extended periods which is isometric exercise. Yoga training has little direct application to any task except yoga- but the benefits of yoga are well suited to help you in a variety of tasks- especially in overall day to day mobility- which is part of why it is so popular. Yoga can be a very comprehensive “functional training” program for general wellness.

If stretching is a little uncomfortable that is ok- but stretching in general- “healthy” stretching- shouldn’t hurt. Most people don’t have to worry about stretching causing problems as part of their regular activities. Those who train very hard- like pro and semi pro level athletes, and those who have health conditions or are at reduced mobility (like those who have not been active much at all for a long time or ever) should be wary- and of course... “before starting a new diet or exercise plan speak to your physician” and all that. But stretching- in a nutshell- can improve or maintain mobility and help prevent injury- when done appropriately.