A therapist will help you work on the various psychological aspects of depression, like intrusive thoughts, past trauma, grief, and so on. On the other hand, the psychiatrist will help you work on the various physical aspects of depression, like hormonal imbalances, sleeplessness, anxiety, and so on.
Self-care includes all the steps you can take to help yourself in your mental health journey. This includes mindfulness, self-love, and so on.
Generally, the best possible outcomes from treatment arise when therapy, self-care and psychiatry work together as they are all complementary to one another.