What is the difference between clinical theory and counseling theory for psychology?

Not a clear question: I'm not sure what you mean, since there are many different clinical theories and theories of counseling psychology. Too numerous to list or explain in 400 characters. The term counseling, as opposed to psychotherapy, tends to be used when the therapist has less clinical training (masters or lower), but this is not always the case.

Too vague: The question is too vague to answer. Clinical and counseling refer to different types of graduate programs, not theories. Clinical psychology programs are generally more competitive and rigorous than counseling psychology programs.

Severity of symptoms: Traditionally, clinical psychologists focused more on patients with severe symptoms in mental health hospitals, and counseling psychologists focused on patients with less pathology with higher levels of functioning. Counseling psychologists also traditionally focused on a patient's strengths and de-emphasized weaknesses. Counseling psychologists also have strong roots in career counseling.