Name is the difference, XML Publisher (today) is only found within E-Business Suite. Prior to release 12, it was added in via a patch. In R12, it comes pre-installed. Both these names can be used interchangeably.
XML Pub operates entirely within EBS and can only be used within EBS. BIP can be installed as a standalone version running off of several OC4J compliant engines, such as Application Server and Tomcat. BIP can be pointed anywhere, so you could do reports out of an OLTP or warehouse database, MSSQL and even within EBS.
Licensing is already included in EBS, and the standalone costs whatever plus maintenance.
BI Publisher is based on OC4J, which is a J2EE compliant engine, which for all practical purposes, is a Web server. You see OC4J in lots of other Oracle products which typically have one thing in common: they expose their application to the user via a Web interface. XMLP is also based on this because EBS runs off of Application Server.
Both include a desktop component, which is an add-in to Word, and the work there is the same regardless of which flavor you’re using. You can create templates and publish them, there being a slight difference in how each version does that.