The difference is subtle. With high order function you coule define (abstract out) a new idiom, while with proper macros you could define a new special form.

In case of using high-order procedure all its arguments will be evaluated in order before application of the procedure while in case if a macro you could explicitly define all the transformations (evaluation rules) for each argument. This is why it is called a special form - it has its own evalustion rules.

Shortcircuiting if or and are canonical examples.

So, with macros you are extending Lisp with new special forms.