As a child, I was very aware of the psychological effect of terrorism - the IRA set off a bomb very close to my home and it was covered extensively in all the media of the time: TV, radio, newspapers.
However, I would argue that putting security theatre into public life has an equally profound psychological effect - it confirms that you are constantly at risk. As a child, seeing more police officers with submachines guns (very unusual at the time) and the removal of rubbish bins and the closing of some roads to cars around where I lived only increased anxiety. As an adult, I'm aware that this too has a chilling effect, but with little benefit gained.
I'll have to politely disagree on natural disasters not being an equivalent existential threat in a world where climate change is increasing their frequency and potency.
A terrorist attack also has a much wider chilling effect for psychological reasons - it represents an existential threat, unlike a natural disaster.