Accounting Date is the date when the entry hits the ledger. Source/Target Transaction Date (also called Expenditure Item Date) is the date when the money was spent, which typically is the date when an item was purchased.
Generally, the Source/Target Transaction Date will be a date prior to the Accounting Date as it can take multiple days for the transaction to flow into the system and hit the ledger. There can be exceptions to the rule where the money is spent for prepayment - and that is why it's important to correctly set the Source/Target Transaction Date for GL to Project transactions in the TOE system.