OS/390 system architecture uses a 31-bit binary numbering scheme. Addressable storage can be up to 2GB where as
z/Series server architecture uses a 64-bit binary numbering scheme. Currently, the largest z900 server has an address space of 64GB.
A key distinguishing point between z/OS and OS/390 is that z/OS can run in what's called z/Architecture mode when running on IBM's most recent generation of processors, the zSeries processors. A key aspect of z/Architecture is that it can perform both 64-bit real and virtual storage addressing (an extension from 31-bit addressing in OS/390).
MVS is the operating system .The OS/390 and now z/OS are packaging techniques whereby you get MVS plus about 60 other "elements" such as System Managed Storage (DFSMS), a Job Entry Subsystem (JES), a security component (Security Server) etc. In effect, what OS/390 and now z/OS are is a method of bundling what used to be (and sometimes still are) many different IBM system software products into a single installation package, which can be installed all at once instead of a product at a time.