The Free On-line Dictionary of Computing (18 March 2015):
An object-oriented application
programming interface (API) derived from NEXTSTEP and
proposed as an open standard by NeXT in 1994.
OpenStep is the specification of the object kits of NEXTSTEP.
OPENSTEP/Mach was an implementation of this specification.
The original, OPENSTEP version 4.0, and really was NEXTSTEP 4.
Rhapsody was the codename for Apple's Mac OS X Server,
which is really NEXTSTEP 5 (it calls itself "kernel 5.3" at
OpenStep was designed to be implemented independently of the
computer's operating system, hardware, and user interface.
The API for Rhapsody will be a superset of OpenStep's.
When the OpenStep API is implemented for a specific platform
and made into a product, it is written in uppercase,
e.g. OPENSTEP Developer 4.2 for Mach, or OPENSTEP Enterprise
for Windows NT and Windows 95. Versions of OPENSTEP exist
for Windows 95/NT, Solaris, HP/UX, and Mach.