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I am a newcomer to WinEdt 7.1 Where can I find a simple explanation for terms such as PDFTeX, PDFLaTeX, and PDFTexify?

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These terms aren’t specific to WinEdt. You might fight some information in Glossary of TeX and LaTeX terms, but this is still very much a work in progress. – doncherry Apr 24 '13 at 19:16
Other than that, you’ll find questions about the specific terms here on tex.sx, with some answers being more newbie-friendly and others less: What's the difference between pdfTeX and pdfLaTeX? ~ Which "TeX" should one use? ~ Differences between LuaTeX, ConTeXt and XeTeX ... Figuring out what all the terms with “TeX” in them mean is probably one of the hardest parts when delving into this world. – doncherry Apr 24 '13 at 19:22

The following, rather than an answer, wants to be a clarification...

While Doncherry is right about PDFTeX and PDFLaTeX, the meaning of PDFTeXify in WinEdt is not what one might think at a first glance.

In fact (taking the term from MiKTeX texify executable), in WinEdt has been implemented a quite sophisticated algorithm which, with one mouse-click, performs all needed compilations to get a fully compiled document.

In other words, when in WinEdt you press the button PDFTeXify (or TeXify when you want a dvi workflow) you launch an algorithm that takes care of compiling the document itself, as well as bibliographies, indexes, glossaries, etc., to get a fully compiled document.

These commands don't necessarily make use of MiKTeX texify program. In fact, they work both with MiKTeX and TeX Live and also succeed where MiKTeX texify fails (eg. when launching biber).

Moreover, these commands are customizable so you can decide, for example, to use makeglossaries for compiling glossaries.

Some additional packages available at the site winedt.org also permit to add additional functionalities to the above commands like compiling nomenclatures, inline asymptote figures, etc.

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