What is the difference between debit balance and credit balance?

This is really not as simple as writing debit balance is or credit balance is:

In accounting Debit literally means the left side and credit means the right side. The difference between a debit balance "account" and a credit balance "account" is:

Debit balance accounts increase with a debit and decrease with a credit

Credit balance accounts increase with a credit and decrease with a debit

Assets maintain a debit balance

Liabilities and Owners Equity maintain a credit balance

The above answer refers to accounting, however, I noticed that you also put this in Credit and Debit cards: using a bank debit or credit card is the opposite of the view you see doing accounting.

On a Credit card statement for example, a credit balance would mean that the credit card company is "crediting" you with a certain amount, meaning you do not owe that amount anymore. A debit would be a rise in the balance you "owe them".