IBM z/VSE is an operating system that runs on the IBM Z hardware platform. This platform is frequently called "the mainframe" which can be confusing as there are a number of operating systems that run on this hardware platform.
z/VSE was originally named DOS/360 and released in 1965. In February 2005 IBM named VSE/ESA 2.7 the successor to DOS/360, then-new z/VSE was named to reflect the new "System z" branding for IBM's mainframe product line.
Notably the list of current operating systems that run on IBM Z hardware include:
IBM z/OS - IBM's flagship business operating system
IBM z/VSE - the precursor operating system to z/OS which is still in use today
IBM z/VM - One of the first level 1 hypervisors that allows for running multiple operating systems on z/OS. This is similar to VMware or KVM on Intel. It provides a set of administrative capabilities to manage storage, CPU, memory and networking.
IBM z/TPF - Transaction Processing Facility is one of the first high throughput systems still in use today in the hospitality, airline and banking industries.