Answer :
They are the same thing. The Enumerated Powers is just another name for the Delegated Powers.
The Delegated Powers are the ones that are specifically granted by the Constitution to the National Government. They are also called enumerated because they are enumerated by the US Constitution and they are divided into three branches of the federal government:
The Legislative Branch has the power to tax, to regulate commerce, to establish weights and measures, to grant patents and to declare war.
The Executive Branch has the power to appoint and receive ambassadors, to command the army and navy and state militias.
The Judicial Branch has the responsibility to decide lawsuits between states and court cases that affect foreign ambassadors.