This summary is not the rule. The rule text controls.
When someone asks a court to end a parent's rights to their child, they have to prove their case with strong, clear evidence. This standard is called "clear and convincing evidence." It's a higher bar than what's used in most civil cases, but not as high as the "beyond a reasonable doubt" standard used in criminal trials. The person or agency asking for termination must prove every part of their case meets this standard.
There's an exception if a parent is accused of abandoning their child. If that parent wants to defend themselves by saying a mental or physical disability caused them to miss out on caring for their child, they only need to prove this with a lower standard called "preponderance of the evidence." This basically means they need to show it's more likely than not that their disability was the reason, rather than needing strong or clear proof.
In short, the parties in these cases face different levels of proof depending on what they're trying to show. The person seeking to end parental rights has a tougher job, while a parent defending against abandonment claims based on disability has an easier standard to meet.