Phone assessment

I had my initial assessment on the phone yesterday with a professional,  we had a long talk about all my childhood and the issues I struggle with now and at the end she told me I was on the Autistic Spectrum. Because I’m at the low end, I may not meet enough criteria to be on a waiting list for a full autism assessment. Even though she assured me she was fully qualified to tell me I’m on the spectrum, and that a full assessment might end with the exact same answer “you’re on the low end of the autistic spectrum” why do I feel like what I’ve been told isn’t enough of a diagnosis :( I feel like a fraud saying the words I’m Autistic because am I? Is saying I’m Autistic the same as saying I’m on the Autistic Spectrum? Has anyone had this answer? I think I just need reassuring.