AFAIK, "Matias Quiet Click" used to be called "Matias Quiet" but it was changed for some reason ... (or maybe I got that wrong ?)
Either way, it is often referred to as "Matias Quiet" within the community, not as the full name.
Glossary of actual keyboard terms:
Clicky: Feedback in the switch sound when the switch actuates in the form of an audible click.
Tactile: Feedback in the switch that you can feel when the switch actuates.
Dampened: The switch has some soft material in it to make it make less of a "clack" when it bottoms out and tops up.
"Matias Quiet Click" is tactile and dampened .. but not clicky.
"Matias Click" is tactile and clicky ... but not dampened.
You could take the "click leaf" from the "Matias Click" and the slider with rubber bumpers from the "Matias Quiet Click" and combine them to make a switch that is tactile, clicky and dampened -- thus making most of its noise when it actuates.
(You could make the similar mod by combining parts from the older Alps Cream and an Alps White.)
BTW. The leaf spring in the tactile, non-clicky Alps switches, Matias switches and in other clones of the Alps is often called a "tactile leaf" as opposed to "click leaf".