Unable to get ANY student overdraft but able to get multiple credit cards?

TLDR: Declined any student overdraft but accepted on 2 different credit cards amounting to a total of £3k with one being the same bank which declined by overdraft application but accepted the credit card.

As stated above I am unable to get ANY student overdraft (Bar the starting £10), being rejected due to my credit limit being below 700 apparently to Barclays - which seems impossible to get for any student regardless.

However, I have been accepted onto 2 different credit cards amounting to a credit limit of 3k which thoroughly confuses me on the credit scoring system and the banks on how they view it when I only wanted £500 as a student overdraft as a 'safety net'.

First, it's quite likely that bank will have one division managing current accounts and overdraft requests on those accounts, and a different division dealing with credit cards. They will each have their own policies on lending. So it's possible to get a credit card with a bank who won't offer you an overdraft, and vice-versa.

Have you spoken to other banks that offer student accounts to see if they can offer you an overdraft facility? You could transfer your existing account (is it a "student" account, by the way? It might make a difference) to the new bank using the Current Account Switch Service.

If your existing account is a student account, have you been complying with it's terms and conditions? Typically these provide that you need to use the student account as your "main or primary" account and to pay your income (e.g. wages, student loan, etc) into it. In some cases you need to be paying in a minimum of £500 per term (easy enough if that's where wages/student loan is being paid). If you're not doing that, then the bank probably won't be offering all the facilities (like an overdraft) you'd typically expect.

Who are the credit cards with? Sometimes they are easy to get as different providers have looser requirements and much higher APR. If Barclays is your bank and rejected you for an OD - they have access to all your banking history and can judge if you are a customer they want or not I’m afraid

I’ve applied to switch from Barclays to HSBC and to no avail, I’ll try again after 2 months but I do use the student account to transfer my student finance into and take funds out for rent but I use my credit card as i get a decent cash back offer then pay it off.

I have 2 credit cards. One with Barclays and one with American Express. It confuses me as it was barclays which offered me a 2k credit limit but refused to give me a £500 overdraft on my student account.