Difference between L14-30 and L10-30 NEMA connectors?
As the Wikipedia article that you linked to points out, the L10-30 is a hot-hot-neutral, and L14-30 is hot-hot-neutral-ground.


  What is the difference, electrically?



The L10-30 can't actually ground an appliance, since ground isn't available.  It uses neutral instead, though that can differ from ground by several volts under normal circumstances, and can be as high as line voltage under certain failure modes.  
The L10-30, doesn't provide a safe means for asymmetric line-to-neutral currents, since the such asymmetry will raise the "ground" potential in the end device (since it's really neutral, not ground).
The L14-30 will support asymmetric line-to-netural loads while maintaining a safe ground (via the separate neutral connection).



  so why does the L14-30 have a separate neutral?



Because it is much safer to have a ground that you can count on to always be at a predictable potential vs. earth ground.



  I also want to know if it's possible to power other split-phase
  appliances in my house with an L14-30 plug on a generator.


That depends on the generator, but yes, provided that the generator has separate overcurrent protection for each phase vs. neutral, you should be able to power split-phase appliances.