To say taking money out of your bank account, we use the verb to withdraw
ELD: Take (money) out of an account.
Example sentence: ‘normally you can withdraw up to £50 in cash’
To say, adding money to your bank card, we use the verb to deposit
ELD: Pay (a sum of money) into a bank or building society account.
Example sentence: ‘the money had been deposited in a Swiss bank account’
Credit goes to @BoldBen who first posted this answer in a comment.
As for to credit and to debit
To credit in ELD: Add (an amount of money) to an account.
To debit in ELD: (of a bank or other financial organization) remove (an amount of money) from a customer's account. or Remove an amount of money from (a bank account)
Debit and credit seem to be used to used to describe transactions between two accounts (not necessarily from the same account holder), while withdraw and deposit are mostly used in relation to case, e.g. transactions in which cash money is taken out of or put into an account.
As they put it here (quote from the article), every credit action has a debit action of the same size associated with it:
'That's why they call it "double-entry accounting." When the cashier is telling you he or she will "credit your account", they are also entering a debit for the same amount that they are not telling you about. The same is true for the debits to your account - there is also a credit being made at the same time.'