(Not meant to be a complete answer, just an addition to others.)
TeX Live provides more secure defaults than MiKTeX and probably pays more attention to security in general. For example, section 3 of this paper describes a simple way to make document (or bibtex database, or package) viruses which would almost make MS-Word look as secure alternative ;-) This attack doesn't work with TeX Live's default settings, regardless of the platform (Windows or other).
Not completely unrelated, TeX Live is designed to support multi-user systems, including being installed on a servers and used on network clients, possibly with mixed architectures and OSes. (Which may be totally irrelevant to the OP, but mentioned only for information.)
Since I'm the author of kerTeX, I will put some precisions about the aim of kerTeX, the present state of kerTeX and the future of kerTeX.
The first aim of kerTeX is and will remain to be able, easily, to obtain what Donald E. Knuth has given us: the TeX system, that is not only TeX but also METAFONT and the fonts. Since the aim of Donald E. Knuth was to be free, to be able to write and produce his books without relying on anyone else or everything else---so that he will not hear anymore that it was impossible to produce his books the way they were done before since the fonts and the layout depended on a technology now orphaned---I find quite scandalous that this series of tools is more and more difficult to obtain and use on whatever system, because the needles are lost in a haystack.
This was the first; and this is still the main purpose of kerTeX.For having a quite confortable minimal system, not only D.E.K.'s programs are provided, but e-TeX (for right to left), MetaPost, bibtex and, of course, dvips plus AMS fonts are provided also.
This goal means too that if I need feedback to adjust the tools for systems I do not use---and I don't want to have the obligation to install all the flavours of all the existing systems because even reporting is too much an effort for people!---kerTeX, by purpose, excludes no system. The minimal requirement is a libc. For building, a subset of POSIX utilities (minimal subset). This means that by cross-compilation, almost every system can be supported. Windows can be supported via cross-compilation with Mingw with some small adjustements---I have simply not the time nor a personal need to focus on that now.
For the future, the next step will be unicode support via utf-8. But I do think that this can be done without huge changes to the core of the TeX program---for the fonts, METAFONT can stay the same, and the "support" will be an external one with tools.
Unicode via utf-8 means some changes relating to the tfm. But once more, this can be done easily by keeping a tfm a 256 glyphes subset, but using a font as a directory. (More on this later.)
What I do not want is to plague kerTeX with external dependencies that will prevent the use of D.E.K.'s programs if these external dependencies are not satisfied. This does not exclude modifications or extensions, as long as the core, the kernel is still available.
I don't want to switch from DVI to PDF natively for this very reason and for licence or copyrights reasons: I don't want to be unable some day to use the programs because some lawying gangs frighten the indirect use of PDF because of some claimed patent infringement.
I have put aside the needles from the haystack. What a huge majority of people will discover is that these needles are in 95% of the cases all they use or need. And it happens that the remaining 5% can be covered without depending on gigabytes of external things.
I hope this clarifies things. (Please don't expect me to participate a lot in threads, since I'm rather busy, with KerGIS, kerTeX and all the rest as, I hope, one can imagine...)
Best Answer
The verb "to implement" means, according to my dictionary,
and it's from Latin implēre (to fulfill), from which also "employ" derived through French.
So "an implementation of TeX" is something that makes TeX (and connected software) usable on a particular machine.
"TeX, the program" is publicly available free of charge and everybody is entitled to use the source for producing derived works. A restriction is that the final product cannot be called "TeX" if it doesn't pass the so-called "trip test".
A program in source code does nothing, what's needed is to adapt it to a processor architecture and to an operating system, so that it can be compiled and made into an executable program. Let's go simple, first, and consider only TeX in the original Knuth form.
One needs to prepare a "change file" where some machine dependent parts must be filled in (I/O and access to time data, for instance). Then TeX can be compiled (often after first translating the Pascal source into C) and run.
However, TeX (the executable) by itself is almost useless. One has to teach it how to access vital parts, such as the font metric data and input files. This is usually done by linking it to a library called
kpathsea(by Karl Berry) during the preparation of the change file or in the compilation process. This library facilitates file system access by TeX and also running auxiliary programs when needed (for instance calling METAFONT when font metric data is not available). It's not the only way: the KerTeX project uses a different library.Having TeX in good shape is still not sufficient. One needs a DVI previewer, a way to produce the needed bitmaps for the fonts, a printer driver, METAFONT. On modern systems, the DVI previewer and the printer driver would be linked to a library for using Type1 fonts.
And that's not the whole picture: nowadays a TeX system should provide pdfTeX, XeTeX and LuaTeX, whose compilation and packing are not easy tasks, considering also what's needed in order to make the complete bundle usable on a machine.
Some "standard packagings" emerged already in the first years of TeX. In the olden days one could get a tape containing prepackaged distributions of TeX for some mainstream architectures: Unix (in some of its variants), Vax/VMS, IBM mainframes. When PC's appeared, some distributions became available on diskettes, free of charge or commercial: emTeX for DOS or OS/2, OzTeX for Mac OS, AtariTeX, AmigaTeX were on the "free" or "shareware" side; PCTeX, Textures and others on the commercial side.
Nowadays the most used implementations of TeX and friends (that is a bundle of connected software for using TeX or variants thereof) are, on the "free" side, TeX Live (Unix based architectures, but also Windows) and MiKTeX (Windows only; a GNU/Linux version had been announced, but never really implemented, as far as I know).