Earlier quoted context omitted.
> “mathematica is a lisp”
http://xahlee.info/M/lisp_root_of_wolfram_lang.html http://xahlee.info/M/lisp_vs_WolframLang.html > WolframLang has all the characteristics of LISP: seems you either don't know what lisp is or you've never written mathematica
Mathematica is a symbolic language based on 'rewriting' There are other examples - Prolog would be an example, a logic language. Also most other computer algebra systems are in this category, similar to Mathematica: Macsyma/Maxima, Axiom, ...
> WolframLang has all the characteristics of LISP
It has many, but there are a lot of differences, too.
The big difference is the actual engine. Mathematica is based on a 'rewrite system'. It translates expressions by applying rewrite rules.
Lisp evaluates expressions either based on an interpreted evaluator or by evaluating compiled code. Lisp has macros, but those can be transformed before the code is compiled or running. The practical effect is that in many Lisp implementations usually all code is compiled, incl. user code. Mathematica uses C++ then. Most of the UI in Mathematica is implemented in C++, where many Lisp systems would implement that in native compiled Lisp.
Thus the computation is very different. Using a rewrite system for programming is quite clunky and inefficient under the hood. A simple example would be to look how lexical closures are implemented.
Another difference is that Mathematica does not expose the data representation of programs to the user all the time, where Lisp programs are also on the surface written as s-expressions (aka symbolic expressions) in text.
The linked page from the Mathematica book also claims that Mathematica is a higher level language. Which is true. Lisp is lower level and languages like the Wolfram Language can be implemented in it. That's one of its original purposes: it's an implementation language for other ('higher-level') languages. Sometimes it already comes with embedded higher-level languages. CLOS + MOP (the meta-object protocol) would be an example for that.