I really like @JeffE's comment:
Most questions, even in the definition stage, seem to be from people who are (or aspire to be) employed in academia (as instructors or researchers), rather than people who are only enrolled in academia (as students).
And I think that is the guideline we should use for higher education means. Basically, education that leads towards academic life.
So a question like
I am a highschool senior aspiring to be a scientist. What should I focus on in undergrad?
Would be more about higher education than
I have a bachelor's degree in accounting. Will a master's program increase my employability in finance?
Even though the second question is about a 'higher level' (Masters usually comes after Bachelors) of education, it is not higher in the sense of not really leading to academic life.
That being said, I think we should be cautious about admission questions and advice for people applying to undergrad.