Depends a bit what you're looking for, as well as on your personal preference and your beta-reader's personal preference.
Generally speaking, a beta reader is the last line before sending the MS to an agent or editor--the term comes from software testing where the beta-test is a fairly open blank-slate test with a large and ideally varied user base. Plonk the software down in front of them, record what happens. Likewise, you want a beta-reader finding the mistakes you couldn't see, not just the mistakes you haven't got around to fixing yet. It's a waste of time if the beta is correcting grammar or formatting when you should have those down yourself through self-editing.
That said, there are alpha readers and critique partners who operate, depending on the partnership, some ways short of the final product. They can be invaluable, providing direction for the writer, initial feedback to influence plot decisions in revision, and so on. But these are fundamentally different people. You need to be able to trust an alpha-reader, the alpha-reader needs to 100% know you and the specific work in question, and often they can help provide momentum and encouragement where a beta-reader provides a look into how the readership for your book will react.
Exactly where you fit into this spectrum is entirely up to you and any potential reader. The rest is more about terminology. If you say you're looking for a beta-reader, I expect you have a finished and polished MS, for instance.
Hope this helps.