Looking around, I have found two different "definitions" for the font generated by the command \mathscr (aka "Ralph Smith’s Formal Script" according to this).
First
from here.
Second
from here.
Questions:
Why are there two different fonts that supposedly come from the same command?
My LaTeX environment gives me the first font. How do I get the second?
The command \mathscr and similiar ones don’t refer to a specific font. If you look at different math fonts like Cambria Math, Asana Math, XITS, Minion Math etc. you see that they are designed with different ideas in mind, hence they look different.
Typing \mathscr just request symbols that look script-like. Of course every font designer has had a different idea what “script-like” should be for his font, thus you get different results. This means that there is no precise definition what \mathscr should look like. Some fonts may not have such symbols at all, some may have more than one, like XITS where you can get a “calligraphic” and a “script” like looking variant of the font.
The actual symbols you get depend on what math font is loaded via \setmathfont in case of unicode-math and LuaTeX or the more traditional NFSS in case of PDFTeX. With NFSS setting the math fonts is more involved. So usually this is done by loading an appropriate package via \usepackage that switches to the fonts in question.
Different packages define \mathscr in different ways.
The first font is defined in the mathrsfs package (I've seen it in many other places as well).
The second font is actually part of the XITS Math font. You can get it by using the code in the answer you linked. You will have to download the font and install it on your system. You will also need to compile your document using xelatex or lualatex.
