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HTML from SGML [ HTML called SGML based , that mean extended from Standard Generalized Markup Language that mean SGML is the father of all hyper text markup languages HTML ] , XML extended from SGML for more special uses even it is extended with less features , XHTML extended from HTML + XML
XHTML5 (XML-serialized HTML5) extended from XML & HTML5
HTML and XML are both markup languages (hence the *ML). XML is a generic markup language suitable for representing arbitrary data, while HTML is a specific markup language suitable only for representing web pages.
HTML and XHTML are both subsets only of SGML, except that XHTML has additional specifications so that it also validates as XML. Think of XML as XHTML's influential godfather.
Because of this relationship to SGML across all3 of these languages, there are a lot of similarities, but they are all considered different languages. However, much of what defines these languages is their restrictions on SGML.
You may find this document helpful, although the technical terms may be hard to digest.http://www.w3.org/TR/NOTE-sgml-xml-971215
XML is not a metalanguage for defining markup languages. Really that's just SGML. XML is simply a data formatting markup language. Your quoted source is using technical terms imprecisely, which is why they are confusing.
Purposes
XML is for defining your own data format. If you wish to pass data between two systems, XML is often the way to do it.
If, for example, you needed to pass a sales order from your website to your billing system, you could create this XML payload:
<order id="12345">
<name>John Doe</name>
<item id="443">Adult Diapers</item>
</order>
Your website would then send that XML to your billing system, which could then parse the data from that XML.
XHTML and HTML are obviously just for web pages. XHTML's primary purpose is to remove a lot of the ambiguity that we had in previous years (decades) of web development. Back in the late90s when I started, we were using HTML3.2 which allowed for seriously sloppy code. HTML4+ and XHTML try to remedy that by either strongly suggesting or enforcing explicit closing tags, explicit attributes, and disallowed tags, which makes it easier on both browsers and humans, and avoids unexpected differences in behaviour cross-browser.