Usually someone who practices Medical Qigong is either 1. A TCM doctor 2. Learned from a TCM doctor a specific Qigong exercise to cure an ailment. However there are some who do teach Medical Qigong to the general public and the line is blurred with other Qigong styles.
Dr. Jerry Alan Johnson wrote like 6 300+ page books on Medical Qigong I don't have them but there is a huge amount of Medical Qigong,Taoist Qigong(he is after all a Taoist priest) I am sure there is martial Qigong(He studies Bagua and I think Taiji among other things)
I don't think I can really say what style or type it is generally up to the teacher who will asses your condition and yes goals.
Alot of it depends on the goal. This is somewhat how the different catagories developed. Taoist aim was Immortality in some way
Buddhist want to be enlighten,Medical wanted to heal and have long life,
Scholars to maintain health and virtue,Martial artist for strength.
And they all kinda of overlap and run into each other.