Most writers I know only refer to beta readers (but then not many of them are writing fan fiction). And those beta readers, like editors, can range from those who just read and give general feedback to those who do a lot more. What you describe as your beta reading is what I do as a developmental editor for people, long before they reach publishing stage, and then as a copy editor. Two different areas of editing to me. I’m curious as to whether you charge for your beta reading services?