Do the momentary pushbuttons also click?
Not ususally. A pushbutton usually has a long
throw with a spring to retract it to its normal (on or off) position. Flashlight 'clickies' do have a tactile feedback, though they are not momentaries.
A tactile switch evolved from the membrane touch switches used originally for keyboards. Without any 'tactile' feedback, membrane keyboards weren't so popular. Someone added a stainless steel dome mounted above the membrane switch, which is a ring and a concentric circle pcb trace activated by pressing a second conductive layer against them. With the satisfying audible and pressure feedback when the steel dome inverts, and the cheaper manufacturing costs, tactile switches became huge.
They then evolved into the plastic jacketed standalone switches that we now are familiar with. The domes are either stainless steel or polyester.