This summary is not the rule. The rule text controls.
Before anyone can testify in court, they have to promise to tell the truth. This can be done through a traditional oath (like swearing "so help me God") or through a simple affirmation that doesn't reference religion. Either option works, as long as it makes the witness understand they have a real duty to be honest.
The point of this rule is to make sure witnesses take their testimony seriously before they start talking. The exact words don't matter as much as the effect: the witness needs to clearly understand they are making a serious promise to tell the truth. Courts allow some flexibility here so that people from different religious backgrounds, or people with no religious beliefs, can all take this promise in a way that feels meaningful to them.
