Math_errors - errors caused by a syntax error in the expression.

Render_errors - tempory errors caused by problems in the rendering process. For instance a tempory drop in connection to a database. These will generally clear themselves after a time as the automatic systems re-rended pages. Often when look at an article in this category but not in the Math_error you cannot even see an error on the page. They can often be cleared using null-edit or a purge.

Render_errors are a super-set of math errors, so if you have a genuine syntax error then it will appear in both categories.

On the English wikipedia we have three categories

https://en.wikipedia.org/wiki/Category:Articles_with_math_errors (Just articles in the Main namespace, & templates)
https://en.wikipedia.org/wiki/Category:Pages_with_math_errors (all other pages, not considered part of the main encylopedia)
https://en.wikipedia.org/wiki/Category:Articles_with_math_render_errors (Render Errors)

Which place they get put in is determined by
https://en.wikipedia.org/wiki/MediaWiki:Math-tracking-category-error
https://en.wikipedia.org/wiki/MediaWiki:Math-tracking-category-render-error