Fear and pinning
Every weapon in Spring:1944 does fear damage. Some more then others, of course. Fear will prevent units from performing certain actions.
Fear has several stages: no fear, under fire/scared and pinned down, displayed as no icon, a yellow star and a red star, respectivly.
The most common example of fear ingame will be found in infantry interactions. When fired upon, infantry will act more causiously. This behaviour is uncontrollable, but, in most cases, desireable.
When scared, infantry will drop to the ground, to avoid stray fire and generally making themselvs a smaller target. As a drawback, they move much slower.
When pinned, infantry become too scared to do anything - you are forced to help them by other means.
Infantry aren't they only units vulnerable to fear damage - deployed weapons and aircraft experience fear as well, but the effects are slightly different. Deployed weapons stop shooting even if they get a little bit scared, so keep infantry away from them.
Aircraft stop responding to your commands when scared and will try to return to your base area. Usually aircraft does not survive long enough to get pinned down.
If you're looking to do some fear damage, you should probably use machine guns, any size will do. They have a small area of effect, but everybody is afraid of them.
Snipers also apply plenty of fear, but usually need some support to actually pin infantry down before they get in range.
Any explosion will scare enemies if they survive the blast.
AA guns are a seperate catagory, while not being particularly scary when used against ground, they have a huge area of effect when pointed at the sky.