'Shutter' shares PIE *skewd- (to propel) with 'shoot' and 'shuttle' — both a closer and a shooter.
Each of a pair of hinged panels fixed inside or outside a window that can be closed for security or privacy or to keep out the light.
From 'shut' + '-er' (agent/instrumental suffix) — literally 'that which shuts.' 'Shut' descends from Old English 'scyttan' (to shut, to close, to bolt, to bar a door), from Proto-Germanic *skutjaną (to push, to shoot, to bar), related to *skeutaną (to shoot, to hurl). The PIE root is *skewd- (to shoot, to hurl, to propel quickly), the same root behind English 'shoot,' 'shot,' 'shout' (to shoot words), and 'sheet' (a cloth shot across a bed). A shutter is literally the thing that shoots across an opening to close it — whether a window shutter sliding across or a camera shutter
'Shut,' 'shoot,' and 'shuttle' all come from the same root — PIE *skewd- (to propel). To shut is to push closed. To shoot is to propel a projectile. A shuttle moves rapidly back and forth (propelled between threads on a loom). And a camera 'shutter' opens and shuts at high speed — shooting and shutting in the same device. The camera shutter is etymologically both a gun