What counts as a liability?
Anything the business is obliged to pay or hand over in future. The obvious ones are supplier invoices you have not yet settled and the balance on a loan. The less obvious ones are tax: VAT collected on sales but not yet paid over, PAYE deducted from staff wages and owed to HMRC, and corporation tax on profits already earned. Money a director has lent the company is a liability too, because the company owes it back.
The balance sheet sorts them by when they fall due. Current liabilities are payable within twelve months — trade creditors, VAT, PAYE, the next year's loan repayments, an overdraft. Non-current liabilities are payable later, which usually means the remainder of a loan or a long-term director's loan.
The split matters because current liabilities are what the business must find cash for soon. Compare them with current assets — cash, debtors, stock — and you have working capital, which is the quickest test of whether a business can pay its way.