From the dfes website, definitions of types of state schools:
Community schools
Community schools are run by local authorities. It employs the staff, owns the land and buildings, and is responsible for admitting pupils. Community schools make strong links with their local community, offering their facilities and providing services such as childcare and adult learning classes.
Foundation schools
Foundation schools are managed by a governing body. They employ the staff, and set the admission criteria. The land and buildings are usually owned by either the governing body or a charitable foundation. By managing themselves, foundation schools believe they can provide the best education for their pupils.
Voluntary-aided schools
Voluntary-aided schools are mainly funded, but not owned, by their local authority. A governing body employs the staff, and set the admission criteria. The school?s buildings and land are normally owned by a charitable foundation, often a religious organisation, and the governing body contributes to building and maintenance costs.
Voluntary-controlled schools
Voluntary-controlled schools are run by the local authority. It employs the school?s staff, and runs the admission procedure. The school?s land and buildings are normally owned by a charity, often a religious organisation, which appoints some of the members of the governing body.