So, what is the difference between an automatic watch and chronograph?

An automatic watch is a self-winding watch, using self-winding movement. With an ability to automatically wind and recharge itself through the motions and movements of the wearers wrist.
A chronograph watch usually has two-three smaller dials on the face that act as stopwatches, these smaller watches don't interfere with the main watch itself.
Simply put, a chronograph is a style of watch dial design and an automatic is a type movement and mechanics of a watch.

What type of watch is more accurate?

While both automatic and chronograph watches are very accurate, there is further functionality with Chronograph watches.
If the chronograph has a tachymeter inscribed along the edge, allowing wearers to convert elapsed time into speed.