You are corrrect. The DSM-5 and ICD-10 are intended to standardize diagnostic criteria. Treatment in determined by the psychiatrist’s and mental health worker’s training and experience.
A psychiatrist has a medical degree and has experience with the medications that might be helpful for the various diagnoses. The mental health worker might be a doctoral-level psychologist or a masters-degree social worker or mental health counselor. How they go about developing a treatment plan is grounded in what school they attended and what theory they embraced as a method for healing. That’s why you hear terms like “cognitive-behavioral,” “psychodynamic,” and “psychodrama.” In addition, therapists often specialize, adding another layer to their approach. Specialties include such things as substance abuse, trauma work, veterans, family or couples work and group work.
So, for example, I describe myself as an Adlerian therapist who specializes in marriage and family therapy. As an experienced therapist (that means an old one), I’ve added other layers of theory and techniques to my approach over the years and I’ve gained experience with the full range of diagnoses. However, my work continues to be grounded in in the theories and techniques of Adler and systemic family therapy. Any therapist should be able to give you a self-description along those lines.
If you are curious about treatment options, you could search various schools of therapy online. One may make more intuitive sense to you than others. If that’s the case, then the next step would be to find a therapist who practices that kind of therapy.
I wish you well.