> It is likely that MathJax tries to use a different font than the one it uses in the test page mentioned above.
No, it uses the same font for the math. The issue is that alignment is very dependent on the font SIZE in use (and how that size maps to the pixel grid of the screen). Try using a slightly larger or smaller font some and see if that helps.
> I want to use exactyle the same font as the test page. How can I solve this?
The test page uses the default browser font and size (since it doesn't set a don't itself). So you would have to not set the font or size on your page in order to get the same situation as in the test page.
Davide