What is meant by "belittling a sin is disbelief, in that one considers it trivial and easy, and commits it without caring about it, treating it like permissible acts in its commission"? And does this differ from the meaning of "treating a sin lightly" mentioned in a previous fatwa?

Sins are not disbelief unless accompanied by something that necessitates disbelief, such as deeming them permissible (istihlal), or belittling them, or disrespecting the Lawgiver. Boasting about and rejoicing in sin may be considered evidence of deeming it permissible. The pivot of declaring someone a disbeliever (takfir) is denial or contempt. The fear is that faith may be removed from one who disregards Allah's command, and sins accumulate upon him until his heart becomes rusted. This matter relates to what resides in the heart; a major sin, when accompanied by shyness and fear, can be like a minor sin, and a minor sin, when accompanied by a lack of shyness and contempt, can be like major sins.