So I learn the difference between petting and patting a dog; and I actually pet the dog more often than pat the dog. I quote the explanations from two sources.
Source 1: From this web page: http://forum.wordreference.com/threads/pat-vs-pet.2286216/
To pet usually involves a stroking motion, whereas to pat involves tapping on just one spot.
Source 2: From this web page: https://answers.yahoo.com/question/index?qid=20110515050230AA5uSZ0
“To pat” and “To pet” are two different verbs, just as “a pat” and “a pet” are two different nouns..
“To pet” is used for a range of physical activities, including patting, stroking – and several other activities when it is petting a human, not a pet!
“To pat” refers to hitting (not violently, though) an object/thing. A kitten pats a table-tennis ball across the floor, you pat your pet on the ribs.