There is no connection between WebMethods and WebSphere products. WebMethods is an ESB made by SoftwareAG. ESB is a generic term for referring to messaging busses (let's say software for transferring messages). Latest version seems to be 9.5. Your requirement is to upgrade their ESB (that is WebMethods) from version 8.2 to 9.5.
WebSphere Message Broker is also an ESB. This one is made by IBM. So is WebSphere Enterprise Service Bus, but this one is made to cover other use cases. The later is discontinued, and the former is being renamed to IBM Integration Bus.