Terry, I checked the statutes written when charters were established.  North Carolina law makes it pretty clear what a charter school is. No mention of “charter-like schools without charters”.  

NCGS ? 115C‑238.29E clearly outlines how a charter school operates:

  (a)       A charter school that is approved by the State
shall be a public school within the local school administrative unit in which
it is located. It shall be accountable to the local board of education if it
applied for and received preliminary approval from that local board for
purposes of ensuring compliance with applicable laws and the provisions of its
charter. All other charter schools shall be accountable to the State Board for
ensuring compliance with applicable laws and the provisions of their charters,
except that any of these charter schools may agree to be accountable to the
local board of the school administrative unit in which the charter school is
located rather than to the State Board.

 (b)       A charter school shall be operated by a private
nonprofit corporation that shall have received federal tax‑exempt status
no later than 24 months following final approval of the application.

 (c)       A charter school shall operate under the written
charter signed by the entity to which it is accountable under subsection (a) of
this section and the applicant. A charter school is not required to enter into
any other contract. The charter shall incorporate the information provided in
the application, as modified during the charter approval process, and any terms
and conditions imposed on the charter school by the State Board of Education.
No other terms may be imposed on the charter school as a condition for receipt
of local funds.

 (d)       The board of directors of the charter school shall
decide matters related to the operation of the school, including budgeting,
curriculum, and operating procedures.

(e)       A charter school’s specific location shall not be
prescribed or limited by a local board or other authority except a zoning
authority. The school may lease space from a local board of education or as is
otherwise lawful in the local school administrative unit in which the charter
school is located. If a charter school leases space from a sectarian
organization, the charter school classes and students shall be physically
separated from any parochial students, and there shall be no religious
artifacts, symbols, iconography, or materials on display in the charter
school’s entrance, classrooms, or hallways. Furthermore, if a charter school
leases space from a sectarian organization, the charter school shall not use
the name of that organization in the name of the charter school. At the request of the charter school, the local board of
education of the local school administrative unit in which the charter school
will be located shall lease any available building or land to the charter
school unless the board demonstrates that the lease is not economically or
practically feasible or that the local board does not have adequate classroom
space to meet its enrollment needs. Notwithstanding any other law, a local
board of education may provide a school facility to a charter school free of
charge; however, the charter school is responsible for the maintenance of and
insurance for the school facility.

 (f)        Except as provided in this Part and pursuant to
the provisions of its charter, a charter school is exempt from statutes and
rules applicable to a local board of education or local school administrative
unit. (1995 (Reg. Sess., 1996), c.
731, s. 2; 1997‑430, s. 4.)