Press the button, the camera takes the picture.
The time between those two events is called "shutter lag".

An old-fashioned film camera used mechanical linkages from that button to the actual shutter. But for the past 25 years, nearly all SLRs have had electronic linkages, film or digital.
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Except that every 36th frame (or less), there's a 1+ minute delay before a film camera can take the next shot.