If she made these comments only to a co-worker I would not be so quick to report her to the State. Pull her aside, explain to her why what she said is incorrect and potentially dangerous and that she is at least violating her own license if not also violating the law. This is a great teaching opportunity to not only educate her on how her behavior damages both professions but also to educate her on how the two roles are different.
If she is telling patients that she is a nurse then I would most certainly address it higher up the food chain and possibly to the State. Impersonating yourself as a medical professional that you are not is an issue especially when it involves the safety of patients.
My concern is that if she believes that she is the same as a nurse but with a different title that she may also be giving patients medical advice, or performing procedures that are not allowed with her license and that is a serious violation of the law as well as patient trust and places the patient at harm.