What really sets the Wolfram language apart is its gigantic library of functions. Want to look up stock quotes? easy. Weather? easy. Plus tons of other built in functions that would make a machine learning prediction of Coppertone suncreen's stock price based on weather forecast a couple of lines. In another language you'd have to set up the API queries yourself with a library, parse the returns with another library, and do the machine learning with another library. Then you'd have to cross your fingers and hope that an API or library update doesn't break your code. Wolfram promises easy access to clean data and much less heartache maintaining it.
Wolfram takes all the building blocks then adds an enormous amount of extra junk that's much less frequently tapped.
Wolfram just renamed it, because Mathematica is only his famous and well-selling product, while Wolfram is himself. :-)
Seeing anyone using Mathematica looks quite similar back in the day to the way Lisp Machines, Interlisp-D and also Smalltalk were being used, by those lucky enough to have access to such systems.
So in experience, it is quite close to Lisp, even if it uses another syntax.