Ledger is what you have.
Running is what been authorized, checks but has not gone through.
What my bank says about available balance:
"The "Available Balance" is the Ledger Balance in an account at the time you opened this page less any amounts that are held (e.g. based on funds availability), pledged (e.g. as security for a loan), or otherwise subject to restraint (e.g. due to legal process or levy). Available Balance may not reflect pending or outstanding transactions.
Ledger: The total amount of funds on deposit for your account, regardless of holds, pledges or restraints.