TeX is an ancient complex program used to produce documents. Unlike modern typesetting programs, you write a text document congaing the text itself and instructions (commands) on how to format the document.
Due to its "generality" and "customizable" character, the set of commands in which the document is written accepts variations. The original set was called "Plain TeX". After it they invented a more structured set called "LaTeX", which seams to be the most popular. (So LaTeX is just TeX but using a particular set of commands). They created an executable (called latex) that implicitly calls TeX using the LaTeX rules, so people tend to forget TeX (seldom used explicitly, but often implicitly).
The program accepts extensions coded in files. For instances, in LaTeX, if one wants to input figures, one can use a "package" called "graphicx" (or other). So a complete system should ship the executables and this extra files (fonts, several packages, documentation). A organized collection of such files for TeX is called a "TeX distribution". Examples of distributions are MikTeX (windows), TeXlive (several plataforms), ProTeXt (windows).
Initially TeX only produced documents in a old and strange format with acronym DVI (DeVice Indepentent). But some day they wrote another program, similar to TeX, which produced PDF files (and DVI as well). This program is pdfTeX. The LaTeX language for pdfTeX is (guess!) pdfLaTeX.
Another extension that can produce text for languages written right-to-left is XeTeX (palindrome name reflect this).
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Summarizing:
Programs: TeX, XeTeX, Omega, etc
Sets of rules for these programs: Plain TeX, LaTeX, ConTeXt. (each gets an executable)
Distributions: MikTeX, ProTeXt, TeXlive, teTeX (outdated).
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A final issue: since these programs have as input text files (often with extension ".tex"), there is a need for text editors. Specialized text editors (front-ends) make the life of using TeX/LaTeX easier, so they should be used. Some come with distributions, like TeXworks. Other famous editors are Emacs, TeXnic Center, Winedt, WinShell, Kile, TeXmaker, TeXshop, and others.