The spindle offsets also influence the Q-factor, or the distance the pedals are away from the seat tube, as well a chainline.
However, for a cartridge, there is only one way to install if the threads are cast into the casing... that is, from the right-hand side of the bike. If the cartridge has sealed bearings pressed onto the spindle, and separate threaded retainers for both sides, then it is possible to insert the cartridge either way. In this case, the long side of the spindle would normally go on the chainring side. Note that I am not talking about the new-wave external BB bearings.