What is a difference between a PBX and Centrex?

a$.$ PBX is the responsibility the subscriber, while Centrex is managed by the service provider

b$.$ PBX services can interconnect local organizational departments within a single building, where Centrex can interconnect organizational departments separated by large geographical distances

c$.$ Centrex is also termed an ACD whereas PBX is only termed a PBX

d$.$ there are not difference between a PBX and Centrex, just the name