Formal Vocational Education in Ireland is a comparatively recent development: the original, academic, 'Established' Leaving Cert was joined by the Leaving Certificate Vocational Program in 1989, and the more practical Leaving Certificate Applied in 1995.
The difference between the LCVP and LCA can be pretty much summed up like this: the LCVP is more business-oriented (tourism, development, business studies), has a language requirement, and still includes some academic elements of the Established LC (students can get into university on the back of it); and the LCA is far more practical, focusing on subjects like agriculture, construction, engineering and some ICT, and enables students to access further education in the form of PLCs, Post Learning Certificate courses.
PLCs have existed since roughly 1985, and are offered at over 200 institutions nationwide. They are typically one or two years long, in a single vocational subject of the student's choice. They contain a strong work experience component as a course requirement. Admission to PLCs is administered by the local VEC (Vocational Educational Committee) instead of the national Central Applications Office for other forms of tertiary education.