What are the three different bookmark features in Safari used for?
Think of it as a hierarchy.

At the top 'level', you have your full collection of bookmarks. This is what's accessed with the book icon and is where you can store, for example, rarely used bookmarks. 

Within this larger collection there is a folder called 'Bookmarks Menu.' You can quickly access anything in this folder using the, well, Bookmarks menu in the menu bar at the top of your screen. I use this for frequent, but not constantly accessed pages. Its the closest analog to how most other browsers handle bookmarks. 

And within that, is Bookmarks Bar. Items in this folder are shown as a bar beneath the address bar for easy one-click access. I keep my most frequently used bookmarks here, as well as things like frequently used bookmarklets.