Richey,
The fields overlap, but are not the same. Physiotherapists have a broader knowledge base, scope of practice and autonomy than athletic trainers, treat the population at large, and focus primarily on rehabilitation. Athletic trainers work just with athletes—granted that's elementary school kids to professional athletes and weekend warriors so a large population as well—and focus on optimizing the athlete's performance, preventing injury, acute injury care, and returning injured athletes back to play as soon as possible.
A physiotherapist who is also a certified athletic trainer is a great combination. Granted I'm biased, but my opinion is that a physiotherapist who is also an athletic trainer is better prepared to treat athletes than either a physiotherapist with a sports certified specialist (sports medicine physical therapist) or an athletic trainer. I base that opinion on my own educational experiences through both an ATEP undergrad and PT school.
It takes four years (maybe five years with the some university are running their courses) to graduate with a BA/BS in sports medicine, kinesiology, exercise physiology, etc, with an ATEP training or a straight BA/BS in athletic training. During that time working in the university's athletic training clinic you'll have figured out whether you enjoyed everything entailed with athletic training or if you found rehabbing the injured athletes to be the most rewarding. If it is the latter consider continuing your education.
If you do continue on to PT school, expect at least another 3 years (5-6 if you go part time). It will be lot more intense in both time and difficulty. But you'd come out a DPT, ATC, be able to get a job almost anywhere, and earn 2-3 times what you would have as new atheltic trainer (though you'd also have a lot more debt.)
Hope that helped.