Bolt actions can be made to accommodate different cartridge lengths.
Long actions are for calibres like .30-06, 270, etc.
Short actions are for calibres like .308, .243, etc.
Some makers also make special extra-long "magnum" actions for long cartridges like the .375 H&H.
A short action might save a couple ounces in terms of weight, but that's about it. Generally, cartridge choice drives action length.