This is a dialect of AsciiMath. The major difference is in the implementation. AsciiMath proper is pretty tightly integrated with MathJax, while this just outputs standard MathML, and then you decide what to do with it.

Second difference is with supported MathML target output. Mathup is far more expressive (we even have tensor index notation in mathup). In mathup you can target your preferred MathML output in a way you can’t in AsciiMath. For example in mathup you can purposefully write any token element you want except <ms>. (`<mi>`, \`<mo>`, "<mtext>", and #`<mn>`), in AsciiMath if you want to wrote Gamma as an identifier (as opposed having it turn into the greek letter) or int as an operator (as opposed to an integral) you have to do it with <mtext>. Here you can do `Gamma` for <mi>Gamma</mi> or \int for <mo>int</mo>.

Thirdly is some differences in syntax. Most noticeable is matrix notation, in AsciiMath you write [(row, one), (row, two)], while in mathup you write [row, one; row, two]. Another major syntax difference is how whitespace works. In mathup you can group pars of your expression together with whitespace, so a+b / c+d is not the same as a + b/c + d. In AsciiMath, you have to use parenthesis to do this.