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Each type of practitioner has a different area of expertise.
These days, most psychiatrists deal mostly with medications. After the initial visit, follow-up visits may be as brief as 15 minutes. Most do not involve themselves in therapy.
A psychologist is a PhD. They cannot prescribe medications, but they are trained in psychological testing and therapy.
Therapists and Counselors (LCSW, LPC) are master's level clinicians. They cannot prescribe meds, and don't do testing. They specialize in therapy. There is no significant difference between the various types of therapists & counselors. Most people start with an LCSW or LPC, and get a referral later to a psychiatrist if they need meds.
There is a way you can look up the therapists that take your insurance and get more information about them to help you make a decision. Many are listed online, and the biggest sites are Psychology Today: http://therapists.psychologytoday.com/rms/?utm_source=www&utm_medium=link&utm_campaign=topnav_find_therapist
and Find A Therapist: http://www.find-a-therapist.com/
Take the list from your insurance company, and see if any of them are listed online. You'll get more information about each one's specialty from their listings and websites.
When you have 3-4 that you are interested in, give each one a call. Briefly describe what issues you want to work on, and ask them to talk a little about how they work with those issues. A conversation will usually be enough to know if you'll be comfortable with a particular therapist.