How exactly does a conference abstract differ from an article abstract?
To me an article abstract summarizes the entire article including the overarching questions through methods, results to the major conclusions. 

A conference abstract will of course also summarize whatever is presented at the conference. The differences lie in several aspects of variable weight:


Conferences are often focused on a specific topic so one can be less stringent with the background
Conference presentations may involve work in progress and as such the final conclusions maybe quite hazy.
The conference abstract may be written before most of the work has actually been done (this is quite common with some conferences in my field) and becomes an "advertisement" for what might come.
The conference contribution may in some cases involve a paper but can also be a poster or an oral presentation. depending on which abstracts may contain varying levels of finalized conclusions.