They all do slightly different things. I ended up with all four because something wasn't working right (turned out to be a problem elsewhere, oops) and having all four doesn't hurt necessarily. It could probably be reduced two two of them and work Just Fine.
Next, there's actually three network methods, not two.
https://github.com/Draco18s/ReasonableRealism/blob/master/src/main/java/com/draco18s/farming/entities/TileEntityTanner.java#L176-L188
One is called when the TE is first created, the other the rest of the time (and no, I can't remember which is which).