What is the difference between saving your ship design and saving as a templet?
Normally ships are designed by the player (at least back in GalCiv 2, maybe not so much in this game). Ships have 2 kinds of stuff you can add to it. First, there is the jewelery and glitter, which determines what the ship looks like. Then there is functional components which determine what your ships can do.
Back in GalCiv 2 original release, players ran into a problem with being able to access their favorite designs. The problem was, when they started a new game, their favorite ships were unavailable because they didn't have the prerequisite techs. You want to use your new fighter ship you designed last game? Tough luck, its not available because you haven't researched photon torpedoes (or some other high level tech). Players got around this by designing their ships without any functional components, thereby avoiding this problem. They just had to be careful not to build their templates (as they didn't have things like weapons to make them useful). Later versions of the game introduced ship templates as way to allow players to keep their favorite ship designs separate from their designs they intended to use.
So to answer your question, templates are a way to keep your fancy ship designs on file, without functional components. You need not look through a list of different ship designs. You only need to have 1 ship template per design. When you want to add weapons and defenses to that kind of ship, you can use a template instead of taking an existing ship and stripping all ship components before you get to work.
This is very much a feature for players who like designing ships that look cool. If that is not your thing, then maybe you won't get much use out of it.