Academies are state-funded schools, that are funded by central government, not maintained by the local councils.
They can choose to deliver their own curriculum and not restricted by the National Curriculum. Their teaching staff not required to have teaching qualifications.
Independent schools are funded by parents and investors and not by central government or local authorities. They can also be charities. They can choose to deliver their own curriculum and not restricted by the National Curriculum
Specialist schools are secondary schools, funded by the local authorities, required to follow the National Curriculum. They are granted a specialist status in certain subjects (e.g. maths, science etc) and can use extra funding to develop the Curriculum in those subjects.
Community schools owned and maintained by the local authority, with links to the community and funds to provide services to it like as night school classes or allowing community groups to use their facilities.
Voluntary schools are usually funded by a trust or religious organisations, which contribute to building costs and influence substantial in the running of the school.
State schools are funded by central government and run by the local authorities. Most state schools have to follow the national curriculum.