XeTeX introduced new primitives such as \Umathcode (up to version 0.9998 called \XeTeXmathcode, renamed for compatibility with LuaTeX) that's the Unicode analog of \mathcode.
What does \mathcode in traditional TeX? A declaration such as
\mathcode`+="202B
tells TeX that a + in math mode should be treated as a binary operation symbol (leftmost byte "2), taken from font family "0 and slot "2B in the corresponding font. In the same vein, one can say something like
\Umathcode`∑="1 "1 "2211
or even
\Umathcode`∑="1 "1 `∑
The primitive \Umathcode has the syntax
\Umathcode<Unicode point> = <math type> <family> <slot>
After the (optional) =, three numbers should be given, because packing the information into a single number as done by TeX is not possible. Actually the information is still packed into a single number (in this case it's decimal 18883089, hexadecimal "1202211), but the translation from packed number to explicit type-family-slot is not straightforward.
This will be probably accompanied by a similar declaration
\Umathchardef\sum="1 "1 "2211
so that typing $∑$ or $\sum$ will give the same result.
The unicode-math package loads a huge list of symbols and performs assignments similar to the one for ∑. The number corresponding to ∑ will be different, because it depends on many aspects which can't be covered in a short answer.
Actually unicode-math does much more than this, because it sets things up so that commands such as \mathbf or \mathrm give the desired result.
There are other primitives corresponding to the traditional ones, namely \Umathchar, for using a directly specified character, or \Udelimiter for setting delimiters with normal and large variant, \Umathaccent and finally \Uradical for defining root symbols. See texdoc xetex that will open “The XeTeX reference guide” by Will Robertson and Khaled Hosny.
Best Answer
The left "tick" is produced by font, either a range of characters of different size and slopes then a vertical repeatable extender, as for extending brackets. The font also specifies the width (thickness) required for the over-bar, which TeX draws in with a rule.
The variant characters for the square roots at different sizes do not correspond to different Unicode code points but will have different glyph names in the font.
For opentype fonts as used by
unicode-math, the information is all in the MATH table which is now part of OpenType but was originally specified in this Microsoft documenthttps://docs.microsoft.com/en-us/typography/opentype/spec/math
In particular here:
radicalRuleThickness