Mathematics layout usually has two different forms: displayed equations (that appear on a separate line, usually centered), and in-line equations (that are part of a paragraph and flow with the rest of the text). The rules used for these two situations differ, in particular for the sizes used in fractions and superscripts. In-line equations produce smaller fractions in order to avoid large spaces between the lines of a paragraph, whereas displayed equations can afford to use more vertical space.
Here is an equation in display mode:
and here is one in in-line mode:
Both where produced by MathJax. In LaTeX files, the distinction between the two is indicated by the delimiters used to identify the mathematics. In-line equations are surrounded by \(...\) or $...$, while displayed equations use \[...\] or $$...$$. In MathML markup, the distinction is made by the "display" attribute of the <math> element: <math display="inline">...</math> versus <math display="block">...</math>.
It looks like your "displayed" equations are being created using in-line delimiters or attributes rather than display ones. Since I don't have access to the page itself, I can't see how the math is actually entered on the page. The editor you use to create the problems may not distinguish between the two forms, and so it may only produce in-line math. I'm not sure why MathType uses display mode here; perhaps it always does that, or perhaps your system produces different output when MathType is selected. I can't tell without seeing the page.
But the problem you are facing is not a bug in MathJax but an error in the way the math is specified on your page.
I do not know how you are producing the math originally, but if you are typing LaTeX equations, you could add the \displaystyle macro to the beginning of the expression to force it to be formatted using the display math rules even if it is in in-line delimiters. That might be an easy fix, and it may be that MathType inserts that for you behind the scenes. I don't have enough information about your system to know for sure.
You also show in-line math being slightly smaller than what MathType produces. That could be due to several causes. One is that MathJax tries to match the size of the mathematics to the size of the surrounding font my matching the ex-height of the math font to the ex-height of the surrounding font. For the Asian font you are using, ex-height may not have any real meaning, so it may not be set to a useful value in the font. (In addition, older versions of IE didn't honor the ex-height of the font, and always set the ex-height to be 2ex = 1em.)
If this is the issue, you could solve it in one of two ways: if you are using v2.3 to MathJax, then you could set
matchFontHeight: false
in the HTML-CSS section of your configuration. That would prevent MathJax from scaling the fonts to match the surrounding text. Alternatively, you could increase the scaling factor by setting
scale: 110
or some similar value in the HTML-CSS section (I see you have it set to 100 right now).
A second possible cause would be if the math is initially in a part of the page that is not displayed (i.e, is in an element with display:none initially), and then revealed after MathJax has typeset the math. In that case, MathJax can't properly determine the size of the surrounding font, and does the best that it can, but doesn't always get it right. If that is the case, let me know and I can suggest some alternatives to display:none. But I suspect the other issue is the real one.
Davide