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XeTeX (/ ˈ z iː t ɛ x / ZEE-tekh [1] or / ˈ z iː t ɛ k /; see also Pronouncing and writing "TeX") is a TeX typesetting engine using Unicode and supporting modern font technologies such as OpenType, Graphite and Apple Advanced Typography (AAT).
TeX Live is a cross-platform, free software distribution for the TeX typesetting system that includes major TeX-related programs, macro packages, and fonts. It is the replacement of its no-longer supported [2] counterpart teTeX. [3]
The latest version of MiKTeX is available at the MiKTeX homepage. In June 2020, Schenk decided to change the numbering convention; the new one is based on the release date. Thus 20.6 was released in June 2020. Since version 2.7, MiKTeX has support for XeTeX, MetaPost and pdfTeX and compatibility with Windows 7. Support for 32-bit computers was ...
I would guess that xetex and xelatex are preprocessors before tex and latex, but there's something with the fonts. It appears that xetex uses user installed local fonts of vector type, and it probably does so on the run, tweaking the behavior of tex/latex to accept the installed local vector fonts. Iff this is the case, XeTeX is phantastiqual ...
AMS-LaTeX and AMS-TeX - classes and packages developed for the American Mathematical Society; extensions of LaTeX and TeX respectively [8]; CircuiTikZ - adds creation of electrical networks (adds on to TikZ) [9]
LuaTeX is a TeX-based computer typesetting system which started as a version of pdfTeX with a Lua scripting engine embedded. After some experiments it was adopted by the TeX Live distribution as a successor to pdfTeX (itself an extension of ε-TeX, which generates PDFs).
The computer program pdfTeX is an extension of Knuth's typesetting program TeX, and was originally written and developed into a publicly usable product by Hàn Thế Thành as a part of the work for his PhD thesis at the Faculty of Informatics, Masaryk University, Brno, Czech Republic.
Beamer can be used with pdfLaTeX, LaTeX+dvips, LuaLaTeX and XeLaTeX. LaTeX+dvipdfm isn’t supported. The standard commands of LaTeX still work. A \tableofcontents will still create a table of contents, \section is still used to create structure, and itemize still creates a list. Overlays and dynamic effects can be easily created.