I believe the 113 is spec'ed for a 1-1/8" diameter seat tube (older steel frames) and the 118 mm is spec'ed for 1-1/4" and 1-3/8" diameter seat tubes (almost all Al and Ti and many newer steel frames).

The longer spindle is needed to get the crank far enough from the seat tube that the front derailleur can reach to small chainring before it hits the seat tube. This is a particular problem with triple cranks.