the head of state and head of government
The president's constitutional roles have expanded in practice to be more powerful than the Founder Fathers intended. These roles include Chief Executive and Commander in Chief.
has the force of law
no, but he made a few appointments to the lower courts which are where the supreme court justices are often taken from.
To advise the president on matters related to executive
departments
generally appointed based on political connections (apex)
To advise the president on matters related to executive departments. -Apex
The commander in chief role addresses major problems while the chief of state role is mostly symboli.