Yes, there seems to be a lot of conflation between the two separate systems (in the media, and in comments on here).
As you say, it’s important to be precise, otherwise people won’t take your arguments seriously. To summarise:
One system involves hash checking. This is performed when photos are being uploaded to iCloud. The hashes are calculated on-device. Private set intersection is used to determine whether the photos being uploaded match anything in the CSAM hash list. Photos that match will be reviewed manually - if I recall correctly, this only occurs after a certain threshold has been reached. This system will only match known CSAM (or whatever else is in the hash list).
The second, independent, system, is a machine learning model which runs on-device to detect sexually explicit photos being received on Messages.app. This system is designed to be run on children’s phones. The system will hide these explicit images by default, and can be configured to alert parents - that feature is designed for under-13s. This system doesn’t use the CSAM hash list.