Sometimes moats were full of water:
Sometimes not:
It was never to do with a “fear of water” just a method of impeding the enemy. In the first image you can see only one clear way to attack the castle. The bridge. Yes someone can cross the water, but once on the other side, in a full suit of armour or drenched in wet heavy leather facing a 20 ft wall? What then? Have you seen the scene in the Holy Grail where Arthur and the Knights attack the castle?
Run away!
One of the main advantages of a moat is to restrict the usage of siege weapons against the castle. In the second image there is no water but it’s still going to be very difficult to get a battering ram to the walls. A moat essentially increases the size of the wall by about another 2 metres. Not only that, but the moat will often be filled with brambles and debris like this:
Getting through a moat is no easy task. Particularly when trying to take a castle and being bombarded by arrows, rocks and hot oil.