What does 常务 mean in an official title?
This term "常务" is originally from a Japanese term "常務取締役". The Chinese and Korean are still using the direct translation. For Chinese, it's "常务董事". 

In an organization, the "常务" is more like "Executive". As the title suggests, they need to participate the daily operation of the organization rather than just providing dispassionate and objective criticism. 

Since "常务" seems closer to an organization from "someone within an organization"'s perspective. So usually "常务" rank higher than normal vice-title.