'Vocational' education is often more related to trades (HVAC or heating/cooling technician, electrician, plumbing, electronics certificate, welding, truck drivers, etc) or sometimes things in the medical field like being a certified nursing assistant (CNA). In the US, often this stuff will be done at a community college or through a particular labor union (pipefitters, steelworkers, plumbers, etc). You may receive a certificate or sometimes an Associate's degree for some programs.There may be local programs through a community college to help prepare people for jobs that are needed locally. Usually this training does not include a Bachelor's degree.
'Professional' usually refers to specific types of university degrees like lawyer, doctor, dentist, optometrist, engineer, pharmacist, librarian, accountant, etc. Often these are advanced degrees that are obtained beyond the bachelor's level.
In the US, high school is 'secondary' school, so it should be 'post-secondary' vocational or professional education to refer to training after getting your high school diploma.