A vocational school, providing vocational education and also sometimes referred to as a trade school or career college, is a school operated for the express purpose of giving its students the skills needed to perform a certain job or jobs. In the US, vocational schools are usually a post-secondary school, but in some instances may take the place of the final years of high school. A vocational school in the Republic of Ireland is a type of secondary education school which places a large emphasis on vocational and technical education. In the UK it would be a college where (for e.g.) you would do a BTEC.
Primary or elementary education consists of the first years of formal, structured education that occurs during childhood. In the UK we call them Primary Schools, in the US and Canada they are Elementary or Grade schools.