What is the difference between sports therapist and normal therapist?

Unclear: I'm not sure what exactly you mean by a "sports" therapist and a "normal" therapist. I think what you probably need to know is that a "physical" therapist is someone who went to school and became licensed or registered as an individual who is qualified to treat a wide range of physical conditions. Just about anyone can call themselves a therapist, so be careful. Google physical therapist.

None really: A sports therapist generally specializes in sports related treatment. However, not all therapists that call themselves "sports therapists" have any additional training than a regular physical therapist.