Any aircraft equipped with ICU or CCU transferring an individual with special medical needs is referred to as a medical flight. There are medical flights that have all sorts of setups onboard.
Men and women that are not able to sit or stand up or are delicate need to be flown in an air ambulance. Many of them simply want to go home to be with their families.
Individuals that are on a respirator need to bring the breathing equipment onboard and also need to be attended by a respiratory therapist. This is along with a regular flight nurse or paramedic.
An incubator and specific apparatus are needed for premature babies. Often babies that are born premature are born in facilities that do not have the resources to properly care for them.
Some who are able to sit up, even for short periods of time, and are not in serious condition, may be able to go on a regular airline. Oxygen supply can even be accompanied, with advance notice. Also, an accompanying medical staff person can go with a man or woman that needs assistance.