No. HTML used to be "an application" of SGML. Meaning HTML brings a profile for SGML features (formerly, an SGML declaration determining things such as allowing tag inference and other minimization) plus a DTD grammar. Though HTML has also quirks for script/style elements, and URLs.
OTOH, XML, like SGML, is a markup meta-language and a proper subset of SGML (also with a fixed SGML declaration disallowing tag inference and almost all other minimization features). XML was introduced by W3C (the SGML "extended review board") as the markup meta-language for new vocabularies on the web going forward around 1997 to eventually replace HTML. While that hasn't happened, SVG and MathML have been specified using XML.
Details on (my pages) below.
[1]: http://sgmljs.net/blog/blog1701.html (the "TALK" slides)
