HTML is a structural semantic Markup Language. HyperText Markup Language, in it's fuller term, was first prototyped in 1980 by Tim-Berners Lee an independent contractor working at CERN. Since it's initial launch in 1989 it has gone on to help define the internet we see today driven largely by the W3C consortium.

The easiest difference to explain is the relationship between HTML and DHTML. Dynamic HTML is a descriptive term for collating various client-side technologies together. HTML can combine Javascript, CSS and the DOM (Document Object Model, a cross platform convention for representing objects in HTML, XML and XHTML). Together these technologies form Dynamic HTML. It is a way of describing this collection of technologies and it's association with HTML.

The differences in XHTML are a little more involved. HTML is based on the Standard Generalized Markup Language model (a descendant of IBM's Generalized Markup Language). XHTML on the other hand is based on an XML model. XHTML can be thought of as the intersection of HTML and XML in many respects. XHTML is still very immature, but the next landmark is actively being worked on; HTML5 and XHTML5.

True XHTML (XHTML2.0) hasn't seen wide adoption. Most developers tending to stick to XHTML1.0 which offers better support for transitioning traditional HTML.

One of the major advantages though, of true XHTML, is speed of parsing (processing information). XML(XHTML) based parsing is quick than traditional SGML(HTML) parsing, but unfortunately not all browsers provide mature support for this. You guessed it. Microsoft's Internet Explorer is one of them.

To quote HTML inventor and W3C chair Tim Berners-Lee's Blog :

The attempt to get the world to switch to XML … all at once didn't work. The large HTML-generating public did not move … Some large communities did shift and are enjoying the fruits of well-formed systems … The plan is to charter a completely new HTML group.

Personally I think we'll see wider adoption of HTML5 than true XHTML.

True XHTML brings about a whole new way of thinking when it comes to writing presentational code. Standard HTML elements that alot of developers are used to are replaced.

HTML forms are replaced with XForms, HTML framesets with XFrames and traditional DOM events with XML Events. HTML5 offers less of a "break from the norm' " and I think, from either lack of understanding, a willingness to self-educate, or promotion of XHTML, true XHTML will not see as wide an audience as HTML5.

We'll see.