Only the specialty. PTs can specialize in a wide variety of things including pediatrics, cancer-rehabilitation, wound-care, neurological/vestibular (helping patients who have suffered strokes or brain injuries), there is even a branch specific to women's health.
Really though, many of the best Sport's PTs chose that path because they love it. If that's the case for you then one option that really works well is complete an undergraduate in Athletic Training and then a Doctorate in Physical Therapy. I would recommend that to anyone REALLY interested in Sports Medicine. Athletic Trainers have a fun, awesome career but are tragically underpaid and since they are not recognized by most insurance companies they have a hard time finding work in a hospital. Being both an AT & DPT would circumvent that and really showcase your expertise in all-things Sports Medicine related.
There are even colleges that advertise this career path and allow you to do both your undergraduate and graduate degree at the same school. Here's one in Boston (https://www.su.edu/athletic-training/athletic-training-programs/dual-degree-doctor-of-physical-therapymaster-of-science-in-athletic-training/)
Alternatively you can earn a MS in Atheltic Training WHILE going to school for your Doctorate in Physical Therapy. (https://www.su.edu/athletic-training/athletic-training-programs/dual-degree-doctor-of-physical-therapymaster-of-science-in-athletic-training/) Google "AT/DPT Programs" for more results.