(1) "Local retirement system" means a retirement system maintained by a county or independent school district for the purpose of providing a retirement benefit program for the teachers and other employees of the county or independent school district.

"Local retirement system" means a retirement or pension system maintained by a county which includes as members thereof county probation and intake employees who become employees of the department as a result of the county probation and intake services' being transferred to [...]

"Local retirement system" means a retirement or pension system maintained by a county which includes as members thereof county juvenile detention employees who become employees of the department as a result of the county juvenile detention services' being transferred to the [...]

"Local retirement system" means a retirement or pension system maintained by a county which includes as members thereof employees of the county boards or departments of health, and the term includes any such retirement or pension system created by law or created by ordinance [...]

(2) "Local retirement system" means a retirement or pension system of a county, municipality, or local board of education which includes teachers as members thereof or which is paying retirement or pension allowances to locally retired teachers.