The subtle difference between retrieve and "get" is that retrieve means to get something...and then bring it back.
Let the prefix re- be your guide here. As it almost always does, re- here connotes a repetition. When you retrieve a memory, for example, you're delving into your mind a bringing that memory back. You're recalling it. And in cases where you're not grabbing something for the second or third time, to retrieve almost always means to get something and bring it to where you are. A natural way to remember the meaning of this word is to note that dogs who retrieve are called "retrievers." They are genetically predisposed to fetch prey and bring it back to their masters.
