Hip rotators

Question on external hip rotators- I am having questions crop up
regarding these, feeling which muscle is activated and stretched, which
is external rotator and which are internal- they are so close together

Indeed in the case of gluteus medius it is both internal and external rotator. One learns this by palpation not so much memorization.

If a student who has good flexibility in the internal hip rotators and adductors comes into baddha konasana and they feel sensation in the
outer hips, is it safe to assume it is the TFL and the anterior gluteus medius?

Do not make assumptions, ask student to show you what they feel. Point to it and then you can identify.

Actually I am the student I speak of. I wondered if what I was feeling in the pose described above is indeed internal hip rotators, but I am unable to differentiate the sensation between the different muscles located in the hip region. So I was trying to intellectualize the experience. So in looking at your answer, should I begin to discern the difference in sensation in the hips from an upright pigeon pose to a folded over pigeon? Will the muscle groups stretching switch from internal rotators to external?

Try to identify muscles of hip rotation via my JFS #5 motion. When you can do that then look at pigeon. Muscles will most definitely change during slight shifts of pelvis especially due to fact that gluteus medius is both an internal rotator (front compartment) and external rotator (posterior compartment)

And if they go into a deeper, less active pose like raja kapotasana preparation, when the body is folded forward over the shin, and there is greater sensation, is it possible that the external hip rotators are being stretched also?

Yes. The body weight creates the stretch. Not the tone of the adductors or internal rotators.