Lisp was invented (or some would say 'discovered') by John McCarthy in the 1960s as a high level general purpose language. He also happened to coin the term ``Artificial Intelligence''. He, his students and his co-workers began using Lisp for their programming tasks and before no time, Lisp got its name intimately entangled with Artificial Intelligence. Lisp, however, is not all about AI; it is a general purpose high level language like C, Perl, Java, and Python. To give you an idea, Lisp is used as the extension language for Autocad, an industry standard CAD program, for Interleaf, a high end publishing program, and of course in Emacs. Lisp was also used by Paul Graham and Robert Morris to build a product that eventually became the foundation of Yahoo Store.
Lisp has evolved over the years and many dialects are in use. Common Lisp, Scheme, Emacs Lisp are, but a few. Some might even say Lisp is really a family of closely related languages. Be that as it may, these days when someone refers to just plain ``Lisp'', she is very likely talking about ``Common Lisp'', if at all she knows what she is talking about; i.e. Common Lisp is the standardised version of Lisp, with formally defined syntax and semantics. What ISO C is to C, Common Lisp is to Lisp.
Scheme is a dialect that eschews the more complex features of Lisp and is widely used in introductory undergraduate courses for students of computing science. Guile, a scheme implementation is being promoted by the Free Software Foundation (FSF) as the extension language of choice for all future GNU projects.
Emacs Lisp is a version of Lisp that has a large number of primitives geared towards text editing needs. A number of other crucial incompatibilities exist between Elisp and Common Lisp, such as the scoping rules for variables. These differences are significant enough to make Elisp a very different and distinct dialect of Lisp, rather than a mere sloppy implementation of the Common Lisp standard (or the precursors to the standard - the two versions of Guy L. Steele Jr.'s publication ``Common Lisp: The Language'')
This article only touches on the basics of Elisp programming. So much so that most of the material here applies to Common Lisp just as much as Elisp. So, from here on, I use the terms ``Lisp'' and ``Elisp'' interchangeably, except where such use will lead to confusion, or there is difference in the behaviour of the two that should be noted.