Yes and no. Expenses can be current liabilities if they are not paid. Similarly, expenses incurred can be non current liabilities if they are expected to be repaid in two years for example.
Expenses are income statement items and if you pay them in cash, there is no liability recorded on the balance sheet. If you purchase items on credit, then yes you will have a liability (which can be either current or non current).
Expenses are income statement items while current liabilities are balance sheet items. If there is an expense that was incurred during the year that had not been paid at the year end, then it will be recorded as a liability. So, expenses that are not yet paid are liabilities but expenses that have been paid are not liabilities since there is no obligation to transfer any additional economic value to the supplier.