Both. Or rather 4 things: One of the things that takes a very long time to develop is reaction time...requires a lot of learned muscle connections and nerve wiring. Those hops over and hurdle and cones with a dives, or going from set position to the side and touch your toes then return to set and catch are all building those connections that help with reaction time, footwork and handling. Next there's also conditioning which develops muscles which other soccer players don't use (such as weights for the arms, squats, ladders, hurdles or crunches). Third there's technique-- where exactly to place your hands or your legs. Fourth, there's tactics and game situational stuff.
The needs of a keeper will change. For example, when they get older more on conditioning and tactics, less on technique (though even technique builds on itself...you shouldn't introduce, for example, tipping over bar until the keeper can perform the high catch, drop step, and punch adequately...you shouldn't introduce the extension dive until the keeper has mastered the collapse dive in the air, which in turn you can't introduce until the basics of diving having been mastered). Different coaches also have different emphasis, which is why I think keepers once they've learned the basics should have a few different approaches.
And this is all separate and apart from field skills, which now days keepers are also expected to master.
