Mathematica is a real functional programming language. It's a lisp with CamelCase builtins and consistent naming. And that's without any of its math goodness. It has superb documentation and a huge standard library. If you master it, you can master any lisp with a simple translator. matlab is a toy by comparison.
Yes, it has lambdas and first-class functions, but that's it. What about closures, for example? Therefore one would better not call Mathematica "a real functional programming language".
BTW, rule-based paradigm and pattern matching is a standard feature of languages from Lisp family, e.g. Scheme. From that point of view Mathematica is not something unique.
Mathematica is a term-rewriting system. This is a fundamentally different model of computation from the lambda calculus.
There are many practical consequences of this, in terms of the design of individual language constructs, and in how the language is used generally.
That's interesting. Can you say what some of these consequences are?