What is Post Secondary Education?
In the US, primary education is the first seven or nine years (depending on location), and secondary education is usually considered high school. Primary and secondary education are compulsory and are provided free by the state (of course some go to private school).

"Post-secondary" education refers to anything you do after that, including bachelor's, master's, and doctorate-level degrees, but also things like associate's degrees and vocational training.

From Wikipedia:


  Higher education (also called post-secondary education, third-level or tertiary education) is an optional final stage of formal learning that occurs after completion of secondary education. Often delivered at universities, academies, colleges, seminaries, conservatories, and institutes of technology, higher education is also available through certain college-level institutions, including vocational schools, trade schools, and other career colleges that award academic degrees or professional certifications. 


If you wanted to distinguish between college or university education and vocational training, you might call the former "tertiary" or "higher" and the latter "further" or "continuing," but it's not a well-defined distinction and not universal.

A master's or doctorate degree is "postgraduate" education.