They are basically the same thing.

Therapists who are not analytically trained and who say they practice psychodynamic therapy often use the term in the broadest sense, which sometimes dilutes the whole concept. I find they usually practice a more supportive type of therapy. Sometimes it does not resemble psychodynamic therapy at all.

Therapists with full psychoanalytic training usually practice it in a more traditional way and it is much more intense imo.

So I think it largely depends on whether the T is a psychoanalyst.

This article explains more about this topic: http://www.jonathanshedler.com/PDFs/...20now%20R9.pdf

I think if you are just starting and already experiencing problems, then I would question if it's a good idea to continue. It could get much worse and even be very damaging.

My current therapist is a psychoanalyst, and he does not recognize a relationship outside of transference, which sounds similar to what you described. Instead, any discussion or requests for modification of the therapy become about my childhood wishes, etc., and become part of the therapy. From my experience and understanding, many, but not all, who are psychoanalytic do this. It's one of the downsides.