What's best treatment for autoimmune thyroid disease and how is the treatment different than typical hypothyroidism?

Most often none: Most often the autoimmune process is not treated. We treat hypothyroidism or hyperthyroidism as those are the important consequences of the process. Treating the process itself with immune suppression is theoretically possible, but not done as such treatments can have serious consequences and in thyroid disease do not offer advantages. The only exception is graves' disease with ocular complication.

Thyroid disease: Most autoimmune thyroid disease needs no "treatment" per se. Chronic lymphocytic thyroiditis, or hashimotos disease is an antibody-mediated inflammation. Monitoring for thyroid function with lab testing and at least once-yearly ultrasound to look for nodules is all that is needed in most cases. This disorder is the most common cause of "acquired hypothyroidism" ie not congenital.