Ammon are the people who had a new king who got poor advice and shamed the messengers of David. I believe after the first campaign, it would have been winter then this battle took place in the spring. Correct me if I'm wrong on that.
For me the key phrases are: at the time that kings go out to battle and David tarried at Jerusalem. It marks a difference in the activity of David. Joab is the captain of the host but usually the king would lead the campaign. David tarried.
v3 "And he brought out the people that were in it, and cut them with saws and with harrows of iron and with axes. Even so dealt David with all the cities of the children of Ammon. And David and all the people returned to Jerusalem."
David also took of Ammon a crown made of a talent of gold inlaid with precious stones and put it on his head.
Next there was war with the Philistines. There was again a giant to deal with. One with six fingers on each hand and six toes on each foot. David had a brother with a son named Jonathan. It was he who slew the giant of the Philistines.
v8 "These were born unto the giant in Gath; and they fell by the hand of David, and by the hand of his servants."
At this point it appears that Ammon has been destroyed as well as the Philistines.
Psalm 107: 39 "Again, they are minished and brought low through oppression, affliction, and sorrow."
Keywords: David, Joab, Ammon, Philistines, Gath. Joab defeats Ammon. Another giant is killed.