I get this question a lot, and with good reason!
In a nutshell, as Athletic Therapists we treat musculoskeletal injuries: that includes muscles, bones, ligaments and joints. We also specialize in return to sport, play, work, whatever that looks like for you.
Athletic Therapists also have training in concussion assessment and management as well as joint taping such as ankles, knees, etc. We get a lot of training in field work where we have our first responder certification and we work alongside a team whether its hockey, football, wrestling, gymnastics etc. In my particular case I used to work with the Hamilton Tiger Cats, so I try and emulate that sport medicine approach used on the players to the general public whom I treat in the clinical setting.
On the other hand, Physiotherapists have a more broad scope of practice which includes musculoskeletal, geriatrics, amputations, cardio, respiratory etc. There are sport-physiotherapists who work alongside teams, however if you are directly comparing the two that is the short answer!