XSLT (Extensible Stylesheet Language Transformations) is a language used to transform XML documents. It is mostly used to transform an XML document into a different XML document with a different XML Schema.
XHTML (eXtensible HyperText Markup Language) is an XML version of the HTML markup language. It was created so websites could be parsed using standard XML processors instead of having to depend on specific HTML processors.
So far everything sounds good, but there are some problems. Following the standard you should be able (as a matter of fact you must) to send an XHTML document to the browser with a mime type of “application/xhtml+xml”. The problem here is that some browsers (IE) don’t understand that mime type and thus don’t render your document.