For every yoga pose, there is a primary muscle you are trying to strengthen and a separate muscle you focused on stretching. They are often antagonistic, whether strongly or mildly. Regardless, you as a practitioner or you as a teacher are asking "why"? Why am I doing a stretch this way? What cues do I give students so they can get the most out of a pose?
Pictured above is a high or crescent lunge (Anjaneyasana). No, this is certainly not warrior I (virabhadrasana A). I was trying to find a version with bent back leg, but nobody posts it that way. But some yoga teachers will offer you to bend the back leg. I think that is OK but it changes the intention of the stretch, and to me, the intention of the pose. I think the primary intention is with the straight leg. So, to answer your question, the primary muscles that are strengthened are the quadriceps of the front leg. The primary muscle being stretched is the psoas of the back leg. "Why" do you ask?
The psoas (pictured below) is a muscle that starts from T12 to L4 of the spine mostly on the transverse processes. It attaches to the lesser trochanter of the femur. They say its the only muscle that connects the upper body to the lower body. That can be debated, but its mostly true. It connects the back to the leg. So since it does, when you bend the back leg, it takes most of the stretch off the psoas and puts it on the rectus femoris. Because of its emphasis on the psoas, I try to make that my focal point. So I insist on a straight back leg. Adding a slight backbend to the pose will stretch the psoas even greater.
Now if you decide to switch the primary focus to the rectus femoris. That’s OK. I think there are better poses for a rectus stretch since the more you bend the knee the better. And if you bend the knee too much in a high lunge, then its no longer a high lunge since your knee will be on the ground. The last two pictures I present will show variations that focuses more on the rectus femoris. The rectus femoris inserts in the front of the hip and attaches to the upper patellar tendon. The patella then connects to the tibia (lower leg). This makes it a two-joint muscle. To stretch the other 3 quadriceps, you just have to bend the knee. But to stretch rectus femoris, you have to also extend the hip forward. Its all biomechanics.
My favorite rectus femoris stretch is supta virasana (reclined hero pose; pictured below). The hip is neutral but in some extension and the knee is heavily bent. I cue students to make sure the baby toe touches the ground. The old school hurdlers stretch with the foot rotated outward is very dangerous to the knee. So I encourage the toes down method. A modification is to do this sitting on the heels and not heel against the hip. But that becomes a different pose; more like a leaning vajrasana (thunderbolt pose).
Another good rectus femoris stretch is couch stretch or King Arthur’s pose. I feel that it is much more uncomfortable because of the pressure on the knee. But it is more modifiable for beginners and can be a very deep stretch for advanced students. In addition, you can place your hip in even more extension with couch stretch (pictured below).
So the bottom line to this story for any pose is, ask yourself what are you trying to stretch and what are you trying to strengthen? Sometimes a practitioner or teacher will modify a pose not really considering these focal points. Anytime you do a modification, does it still meet the intention of the pose? A good knowledge of anatomy goes a long way with yoga. Every yoga teacher who is certified to teach knows these things. But we can all use a refresher now and then.