As I see, both methods use same email massages to cutomer.
Problem is that at Offline Bank transfer we need to show bank data for payment and instructions how to pay. With Cash on Delivery we need just message like "You pay at delivery..."
That's correct. Currently, we only use one content email for all of Offline Payment plugins. If you want to have the separate content for 2 payment plugins, then it requires to customize to the system.