How are the executive departments and the executive office of the president (EOP) different

Executive department heads need approval of the congress and EOP do not.

Explanation:

There are 15 executive departments and their heads conform the cabinet of the president and each head at the same time has the title of secretary. For instance, the Secretary of Education. The difference is that the heads of executive departments need approval of the congress, whereas the executive office of the president (EOP) has as a purpose to provide the president with the best possible support to have an efficient government and do not need approval of congress.

the heads of executive departments need to be approved by Congress, while the heads of the EOP do not.