(Note: The following explanation is specific to TeXLive. I don't know how other TeX distributions -- e.g., MikTeX, PCTeX, Scientific Workplace -- handle this matter.)
You've discovered that there's a single executable program, luatex, and that lualatex is "merely" a symbolic link to luatex. By the way, the single-executable-program-name matter isn't confined to luatex/lualatex: Check out the pdftex/pdflatex and xetex/xelatex pairs.
To understand what's going on, one needs to distinguish between a TeX engine -- an executable program which knows about a number of so-called "primitive" commands -- and a TeX format -- essentially, a group of predefined macros and environments that make the TeX primitives usable for humans. Examples of TeX engines are pdftex, xetex, and luatex, and examples of TeX formats are "Plain TeX" and "LaTeX".
One of the very first steps the engine, i.e., the executable program, does upon starting up is to check how it was invoked. If it was invoked as "pdftex", the Plain-TeX format (purists will want to note that it's the Plain-eTeX format...) is loaded. Conversely, if the command was "pdflatex", the LaTeX (or LaTeX2e) format is loaded. Similarly, "lualatex" loads the LaTeX format, while "luatex" loads the PlainTeX format (which, as you've noted, doesn't recognize the instruction
\documentclass, which isn't suprising since
\documentclass is LaTeX-specific).