These two presidents applied the ideas of limited warfare to Vietnam in ways that were very similar. They varied to some degree as circumstances changed, but they still had similarities. In both cases, the presidents were concerned with ensuring that the war would not spread and that the US would not be seen as an aggressor in the view of other countries.
The strategy of limited warfare in Vietnam always aimed at holding off the Vietcong insurgency while the South Vietnamese government won the “hearts and minds” of the people. The US did not aim to invade or defeat North Vietnam. In this way, it always intended to fight a limited war.
This is why, for example, President Kennedy started out only committing American advisers to Vietnam. He did not want American troops to be fighting because he wanted the South’s government to be able to win the war on its own and gain more legitimacy for itself. This is also why President Johnson never committed to all-out warfare. Johnson, of course, committed more than half a million American forces to Vietnam at one time. However, he still did not contemplate an invasion of the North in an attempt to turn the war into an unlimited war.
So, both presidents applies the strategy of limited warfare by trying to fight the war on as small a scale as possible. The scale of the war increased as time went by, but the underlying goal of keeping it as limited as possible always informed American actions.