So how do TEX and LaTeX fit into this concept? Let us first look at TEX, and then at LaTeX.
TEX is a computerized typesetting system, geared towards the typesetting of manuscripts which contain a lot of mathematics. Like the traditional typesetting systems, TEX requires information from the user about where and how things are to be put on paper. TEX provides many basic commands, but these commands are hardly ever used directly. The commands are grouped in macros, which perform (typographically) logical functions. Macros are grouped into macro packages. TEX comes with a standard macro package `plain.tex', and it is this macro package that is used by most authors who say they use TEX.
However, this `plain' macro package still requires information from the user about where and how things are to be put on paper. And it is here that a problem arises. Because if `plain' TEX were to be used for scientific publishing, it would mean that authors have to concern themselves with the layout and the typographical details of the journal(s) they are publishing in. Although publishers would not dare to doubt the scientific capabilities of authors, they have serious concerns about their qualities as typographers. And with good reason, as years of experience with `camera ready' manuscripts have shown.
But, because TEX actually is a computer programme, there are great powers hidden inside. By building on the `plain' macros, or by developing completely new ones, the concept of macros can be carried further, until a package is achieved which, to the user, looks like a `Generalized Mark-up Language'.