Difference between sessionTransacted and JmsTransactionManager

Correct.

On the DefaultMessageListenerContainer(DMLC) you typically only need acknowledgemode=transacted; you would only use a transaction manager on a DMLC if you need to synchronize the JMS transaction with, say, a JDBC transaction or you need to use a platform (JTA) transaction manager.

Further, any downstream JmsTemplate operation on the container's thread will be done in the same session and participate in the transaction.

Similarly, for JmsTemplate operations on a thread that is not a container thread you generally don't need a transaction manager, unless the platform requires it.