Tax status as a funded PhD student

Hello, I've got a few questions about the tax status of being a funded PhD student, which I'm sure will have been asked and answered before. The first one is to do with income; I'm occasionally asked whether I'm a student or employed and I'm not really sure what to put but tend to lean towards student as I've been told that a studentship isn't employment, strictly speaking. Following on from that, I've been asked to do a bit of part-time work at the university's open days. By signing up to their payroll, does that make me employed and does that have any effect on my tax status, i.e. will I need to start paying council tax? As far as I know, being a registered student will prevent me having to pay council tax.

Thanks in advance!

As a registered student you are exempt from council tax regardless of work you do on the side.
If you are receiving a stipend for your PhD, that will be tax free and you dont need to declare to anyone.
Your job title, if you need one, is student.
You will have to pay National Insurance on your earnings from payroll work but the uni will sort that out for you. Depending on your tax code you may also be paying tax but in April time you will get that refunded to you by HMRC.