I will try to explain (probably with many imprecisions: sorry for the
purists) making a parallel with programming... so I hope you know the basics
of a programming activity.
TeX and LaTeX are typesetting languages. 'tex' and 'latex' are the names of
the commands to interpret the TeX or LaTeX languages. They turn the text
into a DVI file, which is then usually turned into a PDF file with 'dvipdf'
('pdflatex' directly produces a PDF file). Like a compiler turns a source
code into an executable binary.
LaTeX can be considered a superset of TeX, like C++ is a superset of C. You
certainly want to learn LaTeX and not TeX. For the same reason that you
should styles in LibreOffice: in LaTeX, you write what you want and not how
to do it (as in TeX), hence focusing on the content.
LaTeX is extensible with packages, the equivalent of a libraries in a
programming language. And there exist many fonts. And independent tools
(e.g., BiBTeX for formatting references). The so-called LaTeX distribution
group all that in a coherent whole. You want to rely on the "TeX Live"
distribution. It is the best LaTeX distribution, it is packaged in Trisquel
in many parts. In this way, you do not have to install all "TeX Live" to
only use a tiny part of it. The "texlive" meta-package depends on a
reasonable subset, i.e., triggers the installation of all the most popular
packages. But there is "texlive-full" too, if you want.
To write the text that will be interpreted with 'latex' or 'pdflatex', you
can use *any* text editor, like you can use any text editor to write in C++.
However there are sorts of IDE or LaTeX. That is what we were discussing.
