Exploratory
Exploratory surgery and foreign body removals are somewhat linked together. Usually and exploratory is performed when there seems to be some unusual blockage in the digestive tract. This could be due to a foreign body, or inflammation, etc.
Foreign Body Removal
There are occasionally some things in your pet's belly that shouldn't be there. This is usually taken care of with an exploratory. There are other types of foreign body removals--like foxtails in the feet or eyes or nose, fish hooks in oral cavity/face/feet, bladder stone removals etc.