The State Board of Nursing has standards that a school must meet in order for its students to be eligible to be licensed in that state. Those standards are the bare minimum
that a school must meet in order for its graduates to be legally allowed to take the test, get a license, and work as a nurse (LPN or RN) in that state.
A lot of students mistakenly believe that the State Board approval us all that counts -- and/or that it represents the highest level of quality in the education world. That is not correct, as explained in the above paragraph.
Other organizations and agencies provide other sorts of accreditations that reflect the values, scope of service, and standards of each particular organization or agency. Some of those organizations are nationally based and some are regionally based. Some are focused only on nursing. Others focus on all types of education. Some are focused on "vocational" education while others are focused on academic or scholarly education. etc. etc. etc.
Each school has choices about which types of accreditation to seek. They tend to choose organizations that focus on the type of teaching program they wish to provide. For example, a vocational school would seek accreditation from an organization that focuses on vocational education while a university would probably seek accreditation from an organization with a more academic focus.
In nursing, there are 2 major organizations that provide accreditation for schools
of nursing -- the NLN and the AACN. The AACN is an organization representing colleges and universities and its standards reflect the values of those in higher education at the college/university level. They do not accredit schools that are not located in a college or university. It is the "gold standard" for BSN programs. The NLN accredits BSN programs, but it also
accredits programs that are not located in colleges or universities -- such as diploma programs and/or programs in vocational schools.
Both the NLN and the AACN are nursing organizations and their standard incorporate nursing values and ideals. The vast majority of reputable nursing schools are accredited by one of these two organizations. It's a "seal of approval" that shows that the school has met the standards of the nursing profession that are more rigorous than the minimal standards set by the State Board.
Some schools choose not to seek accreditation from either organization. They are accredited only by the organizations that provide general accreditation for all types of schools. So, they can rightly say that they are "accredited" to provide education and therefore their students are eligible to receive finanancial aid from the government. But that type of accreditation says nothing about the nursing
aspects of their program and whether or not it meets nursing
standards. Such programs have not been evaluated by a nursing organization except for the minimal assessment done by the State Board. If you graduate from such a school, you will be able to legally practice nursing ... but your education may not be given as much respect when you apply to other schools to further your education. Some hospitals may also question your level of knowledge if they know that your school did not meet the higher standards of the nursing profession. Some schools and some employers will not care one way or the other.
I hope that explains it.