Maxima inputs and outputs



As part of my study assignment I am trying to understand what goes into and 
what leaves Maxima.

I have seen that when I from the command line enter an expression, as a 
string of ASCII characters, Maxima presents the return in ASCII characters. 
When I use Xmaxima as interface I get the exact same output in the Xmaxima 
text window.

However, when I use wxMaxima as interface, although the input is the same 
string of ASCII characters as in the Maxima command line (and Xmaxima) the 
output is shown with two-dimensional mathematical notation in reasonable 
quality typeset.  For example the square-root symbol expands with the size 
of the expression for which the square-root is taken.  I am aware that it is 
the wxmaxima file (...\Maxima-5.15.0\wxMaxima\data\wxmaxima) that converts 
the return to a format that resembles MathML and that format generates the 
mathematical notation output.

Then in the TeXmacs-Maxima interface (by Andrey Grozyn) I form the input in 
mathematical notation built up according to the semantic structure of the 
expression and the return is likewise shown in mathematical notation.  I 
have seen that the input generates a source-tree and that a similar 
source-tree is generated that drives the mathematical notation of the 
output.

My question is now whether Maxima in all cases produces the same return. 
For example does Maxima return to wxMaxima the same ASCII-character output 
as goes into the command-line or does wxMaxima load wxmathml into Maxima so 
that the return wxMaxima receives has already been converted to the 
MathML-like format?  If the latter, what is it that is presented to 
wxmathml?  Is it Lisp-expressions or ASCII-characters or what?

In addition to these specific questions, because there is a budget available 
I am looking for more general tuition on how I can follow the flow in and 
out of Maxima, how to decipher wxmathml, etc.  I have tried to study Lisp, 
MathML, Tcl, etc. but that is difficult due to my lack of technical skills. 
I hope that someone can point me in the right direction on that one.