A private school is a private school: parents pay tuition, the school selects which kids are accepted and which are not. Hyde School, North Yarmouth Academy, The Center for Teaching and Learning. A public school is, in theory at least, open to any child who lives in the area which that public school serves - and that applies to public charter schools as well. No examples in Maine, 4,936 examples in 40 other states.
Public charter schools are, according to National Alliance for Public Charter Schools:
"independent public schools that are allowed the freedom to be more innovative, while being held accountable for improved student achievement.
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tuition-free and open to every student who wishes to enroll
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non-sectarian, and do not discriminate on any basis
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publicly funded by local, state and federal tax dollars based on enrollment, like other public schools
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held accountable to state and federal academic standards"
Some states allow schools that have previously operated as private schools