When I first read your first post, my first thought was "does it actually matter what your dx is?" And yeah, I get it. It can help to know. But a lot of mental health and medical health issues are inexact. The label isn't what tells you whether you deserve to be feeling pain. The label is a tool so you can understand, treat, and communicate about your pain.
Look at something completely different. I was told I probably had fibromyalgia. I went to a specialist who said "nope" you have chronic myfascial pain syndrome. Another doctor, who wasn't a specialist said it probably was fibormyalgia. My chiropractor said none of it fits me. And for neither condition is there (currently) a definitive test. Doctor's can do an exam, but it's not the same as a decisive blood test or x-ray where there's no doubt. So where does that leave me? I could go to another doctor and get another diagnosis potentially. I could obsess over what I have. I could feel like I must be a fake, liar, drama king etc.... and to be fair, in my darkest moments I do. But the reality is I have pain most of the time. I have fatigue. My muscles knot up like crazy. I tend to use the chronic myofascial pain explanation when talking to medical people because it seems to most accurately describe what I experience. When talking to non-medical people I sometimes say fibro, because chronic myofascial pain syndrome is too freaking long to say and no one has ever heard of it. Knowing that one (or both) of those labels might apply to me, was useful because then I could learn what could potentially help me. I could learn how to care for myself. But those labels don't define me. And if both of those labels went away, my pain and other symptoms aren't going to go magically away (I wish!).
Its important to me because all the books I read about complex trauma resonated with me.
Great, it resonated with you. That means there are things you can learn from it. I have read books about being deaf. There are things there that resonate with me. Not only am I not deaf, I have better than average hearing. Does that mean I'm wrong to take away some learning from the books I've read? And I'm not saying that you don't have complex PTSD. I'm trying to let you know, your experience is real. Even if we called it the floopy disorder, all the feelings and struggles you have still exist and still matter. And you are not evil or a fake.
And obsessing over the exact thing he said, isn't going to help you. As I read everyone talking about parts, I was getting concerned that we were sending you down a rabbit whole because we don't know what he even meant by parts. And don't forget, your T was responding to things you said. In your original post, there is mention of complex trauma, complex ptsd, development trauma, parts (whatever was meant by that) and more. Do you know how easy it would be for one of you to mishear each other or misspeak? All it really means is you and your T have a lot more conversations ahead so you can both gain a better understanding of you and work towards the real goal, of helping you heal from your very real pain.