Recipes for preserving tend to be very specific. They're calibrated to balance factors like pH and sugar content in the final recipes, and of course to minimize the risk of spoilage. In general, you should always follow the steps as written in your recipe.
What I've generally observed is that jam-type recipes don't always include the final boiling step because the jam is already cooked (edit: and because per rumtscho, the sugar content is generally high enough to be inhospitable to bacteria). That differs from canning fresh fruits and vegetables which are largely raw. The purpose of the boiling step here is to kill off pathogens before they get a chance to settle in and spoil the contents, as no matter how well you clean them, there are likely to be some spores, bacteria, etc. remaining. Even a tiny initial population can grow and spoil your preserves over the length of time they'll be put away.
So, initial sterilization is always required to clean the jars themselves. The second boil pasteurizes the contents. If you've already done this as part of your preparation, as with a jam, then it most likely isn't required. It probably won't hurt, especially if you plan to put up your jams for an extended period of time (i.e. months or years) but you'll have to weigh the convenience of skipping that step against the potential risk of spoilage.
That said, let me state again for the record that if your specific recipe says to include the final boil, then there's likely a very good reason, and you should follow that instruction.