The shift cable, regardless of front or back, pulls against a spring in the derailleur cage to move the cage and thus move the chain into a position to either climb onto the next bigger gear or fall off onto the next smaller gear. If you have indexed shifting the shift lever mechanism has built into it detents that click into place to allow the cage to move the exact amount to get the chain to climb or drop one gear per click. When set up properly if the cable is set for one gear all gears will be set.

A quick quiet shift is the goal. The higher quality derailleur/shifter combinations are made with such precision that this is normal for every gear. The middle grade parts can make a few good shifts somewhere in their range but the rest are just so so. The low quality parts can’t be adjusted to make good shifts only lame attempts to successfully move the chain to the different gears with an abundance of grinding and gnashing.