Physiotherapists are trained to cover acute and chronic injuries to the structure of the body (MSK) and how to recognise the multitude of medical conditions with which they could be faced with in a hospital.
Sports Therapists are trained to deal with acute trauma, typically as would be found pitch side. In this situation at a major club, a Sports Therapist would work alongside a medical Doctor and Physiotherapist.
Recently I discussed roles with an Olympics Physiotherapist, and he felt Sports Therapists were excellent at pitch side care, having good relationships with the players. They would routinely deal with acute trauma and CPR. They are used to assess essentially healthy individuals with acute injury.
They can diagnose sports injuries and prescribe complex rehabilitation programs to aid recovery. They know when and how much sport to return to as the injury heals and have knowledge of massage, nutrition, preventative care and how to stay well.
Physiotherapists are not able to prescribe sports-specific rehabilitation programs unless trained postgraduate in sports medicine. They can however triage sports injuries, head injuries, spinal problems, neurological problems, and respiratory and rheumatological problems.
A Physiotherapist will often triage and then refer a patient to a Sports Therapist for massage and rehab.