Both professions have similar objectives, but, their 'toolbox' is different.
A physiotherapist focuses on relieving pain through soft tissue work, trigger points, electrotherapy, acupuncture, etc. In some jurisdictions, they can also prescribe medication.
A Sports therapist and Physical therapist focus on the 'cause' of the problem. Their interventions include; fixing flexibility restrictions, balancing asymmetries and strengthening weak muscles, for example.
A Sports med doc. can do the above, as well as administer drugs.
All these professions deserve equal respect. If they could combine their 'toolboxes,' we would end up with a 'workshop' for the injured.
The future of healthcare will involve many specialized individuals combining their expertise to give the best possible care.
Awesome answer, thanks heaps :)