Push button switch with "hysteresis"
I'm not sure of the distinction you are trying to describe. The 6mm x 6mm tact switch you show and the microswitch both have an audible click when released, and in both cases it will likely be a bit later (some milliseconds) than the N.O. contacts opening. 

In the first case it's caused by the internal metal dome contact oilcanning back to the rest position and in the second case it's probably caused by the N.C. contacts slamming together. Here is what the contact inside the tact switch looks like (from this website) - the mark in the middle is where the button presses on it to oilcan it downward and make contact: 



The "tact" in the tact switch name is from the tactile feedback it gives you, unlike a membrane switch sans dome which provides no feedback. Many modern membrane switches incorporate a metal or plastic dome that gives you feedback, and in that sense they are much like the tact switch. 



One generic term is "snap action". But maybe @SteveG is right and you are conflating the relatively loud door latch snap action with that of the interlock switch. 

If so, its not a characteristic you will find in a common inexpensive component, it's a separate mechanical contrivance and just happens to carry the switch operation along for the ride.