What is the difference between Grills, Barbecues, Broiling e.t.c.?
As Mien pointed out in the comments, these terms can vary based on where you are from. My answer is based on the U.S. version of the terms. 

Grilling: To cook with direct exposure to heat, usually from below.

Broiling: To cook with direct exposure to heat, usually from above.

BBQing: To cook with indirect heat using wood in order to add a smoke flavor. 

In many parts of the U.S. grilling and BBQing are used synonymously, in which it mostly implies grilling meat outdoors, although, as you can see by the definitions above, that isn't entirely accurate.