I'm trying to answer it in a simple way utilizing Wikipedia:
That means that MathJax is a software that works in your browser on some text which is marked up using different techniques. One of them is a LaTeX-like notation. In general it is independent of usual LaTeX binaries and the most part of the markup LaTeX provides.
LaTeX on the other hand is referred to as document preparation system. It is also used as term for the markup language that's used to write the document. In general LaTeX is a) a TeX format (so the markup language) and b) an executable that processes documents in (a) into the DVI format.