Words can have very specific meanings when describing medical diagnoses, and slightly less so in general usage describing social distinctions. For individual people, words mean to you whatever they mean. Transphobic people may toss out things like "trans women are not REAL women," without offering an explicit definition of what a "woman" is in their opinion other than "born without a penis." Are they incorrect? Well, according to their definition of "woman," no, but that's THEIR definition.
My understanding of "intersex" is one thing if used as a medical term, but more expansive and fluid if being used by someone to describe their own identity. In general, if someone is claiming a label like "intersex." unless you are a clinician charged with their care, and maybe even then, I would defer to their own assessment.
A good rule of thumb regarding labels is that they are best used as "descriptive," rather than "prescriptive," That is, one ought not determine "oh, I am transgender, and therefore I ought to do..." Rather, find a label that seems to describe you as you are, and to find others identifying similarly. Share experiences and learn from each other. Talk with others identifying differently, maybe discover some new facets of yourself you hadn't seen before.
Erin