Should I Install LaTeX , MiKTeX or TexStudio?

In various guises, this is a common question, seemingly innocent, but actually betraying a fundamental confusion about LaTeX directory, and the levels of operation in the TeX World; concepts, distributions, distributions, variants and the TeX family and friends (i.e., users, contributors, dependent and extended language & softwares). TeX is a typesetting language developed by Donald E. Kunth, today's worldwide de facto standard for high quality document typesetting.  LateX is a Tex based typesetting system and collection of macros for document compilation and publication - not a word processor. MiKTeX is a compiler and an  Windows O/S based TeX/LaTeX distributions. The purpose of this read is to clear the confusion and give a comprehensive introduction to the World of LaTeX, hence provide information and technical bases for anyone, authors including academias to choose between LaTeX/Tex distributions to install given the features of the offered LaTeX engines and Compilers needed by their project or document typesetting. This fills the gaps in knowledge and literature, aside numerous plagiarized blogs , confusing articles (as learning latex itself) , confusing articles (as learning latex itself) and guidelines relating to scientific typesetting, LaTeX distributions, .tex editors, LaTeX distributions, .tex editors, Latex2e, LaTeX3 and the the LaTeX family.