The general correlation between these two things is that the limited war ideology led to a set of rules of engagement that were rather restrictive. These rules of engagement were seen to be necessary in order to keep the war limited and to accomplish the goals of a limited war.
In Vietnam, the goal was not to invade the North, take territory, and win the war in that way. Instead, the goal was to win the “hearts and minds” of the Vietnamese so that they would support the South’s government rather than supporting the Vietcong. It was also important to maintain the US’s positive image on the international stage so that our allies would not put pressure on us to leave Vietnam.
Because of these limited war goals, the political and military leaders of the US drew up restrictive rules of engagement. It was important to avoid looking as if we were waging an aggressive war. It was also important to avoid (or at least to try to avoid) doing harm to the average South Vietnamese person since it was that person’s “heart and mind” that we were trying to win. These rules of engagement were devised as a way to allow the US to fight, and hopefully win, a limited war.