These Fender® style saddles allow for individual string adjustments, meaning both the individual string height and length are adjustable. The 2 Allen head screws in the front of each saddle serve as "feet" which lower or raise the saddle thereby changing the height of the string above the fingerboard. The long, Phillips head screw thru the center moves the saddle fore and aft and controls the strings individual scale length. Adjusting a strings length directly effects intonation.
Here's an example of the Gibson® style ABR® or Tune-O-Matic® (TOM) bridges. Instead of adjusting each individual saddles height, the bridge is adjusted as a unit by turning the 2 outer thumbwheels. The flat head screws which pass thru the center of each saddle allow us to move the saddle fore and aft. That movement changes the strings overall length and affects intonation. The thin retaining wire used on many of these models keeps the saddles from falling out when the strings are removed. Read about Tonepros® ABR® bridge replacement for Gibson® guitars.
Floyd Rose® style Tremolos often look intimidating but they are more frustrating than anything else. The screws which I labeled string clamps are long Allen head screws which tighten against a small block that wedges or locks the end of the string into the tremolo, ball ends must be clipped from the string when used with this style of tremolo. The flat, knurled knobs are fine tuners. These tuners mean we can avoid loosening the screws on a locking nut each time we tune up. The 6 Allen head screws you see in front of each saddle are only loosened when making adjustments to intonation. When loosened the saddle can be moved back and forth changing the strings overall string length and adjusting intonation. The 2 flat head (or allen head) screws I've labeled pivots raise and lower the bridge as a whole as well as serve as a pivot point for the tremolo to rock on when in use. Read more about adjusting Floyd Rose® Style Tremolos