Looking at the two poses you can see that in the first pose, bound angle pose, the hip goes into flexion, abduction and external rotation.
In the second pose, the hip is flexed and abducted, but appears to be in neutral rotation.
So it would seem that the key to your difficulty with the first pose and not the second is the inability to externally rotate the hip. If the reason is structural - the way your femur is formed, then stretching exercises will not change your ability to externally rotate significantly. If tight muscles are the cause, you can make changes over time.
Tight internal rotators could be the limiting cause (by limiting the external rotation). There are several muscles that contribute to internal rotation of the hips:
• the anterior fibers of the gluteus medius and minimus (as you have noted are the area you feel pain)
• the tensor fascia lata (TFL)
• medial hamstrings
Additionally, other muscles like the adductors contribute to internal rotation depending on the degree of hip flexion. The hip muscles often have more than one function depending on the direction of the fibers or the position of the hip.
To lengthen these muscles you can use stretching and massage. PNF techniques like contract/relax or hold/relax can help with your stretching. Here is a nice article for releasing hip internal rotators with yoga in mind.
Tennis ball massage will also help with the release of tight muscles - placing the ball on the belly of the muscle and then relaxing some of your body weight onto the ball. This video demonstrates a TFL release.
You can also use the tennis ball approach for the gluteus medius. Similar to the video for the tensor, lie partially on your side rather than on your stomach. Place the tennis ball just in front or in back of your hip and the point of tension on the soft tissue, not on the bone. (You have identified the point of tension in your diagram.) Then slowly roll some of your weight forward or back onto the ball being careful not to cause pain. Do not overdo. Only put as much weight on the ball as is comfortable. You can release the medial hamstrings with the ball or with a foam roller. Massage therapy may also help.
Hopefully with stretching and massage you can release the muscles causing you pain.