XMPP is the new name, Jabber the old. So yes, they refer to the same protocol stack.
XMPP is used as name since 2002:
In late 2001 and early 2002, prominent members of the Jabber community
decided to once again submit the base Jabber protocols to the IETF,
this time as an official submission by the JSF. The first submission
was made in February 2002 as an informational Internet-Draft (text |
HTML). Following on the success of this submission, it was decided to
explore the possibility of forming an IETF Working Group devoted to
formalization of the base Jabber protocols, under the neutral name of
Extensible Messaging and Presence Protocol (XMPP).
Maybe some background: The name/term 'Jabber' was bought by Cisco and is now a registered trademark of Cisco.