It is frequently asked about the difference between the above mentioned operations. It's indeed simple. Lets take the example of a cylinder and a box that you want to join together.
-\section Fuse
+\b Fuse
The \b fuse operation will make a <b>single solid</b> from the two given solids :
\image html fuse.png
-\section Partition
+\b Partition
The \b partition operation will do basically the same but it will <b>keep a face at the frontier between the two solids</b> (in brown on the picture below).
This face is shared by the two solids, which means that this face is present only one time in the resulting shape and is a sub-shape of the box and a sub-shape of the cylinder.
\image html partition.png
-\section Compound
+\b Compound
When you build a \b compound by using the build -> compound operation you just make <b>an object that contains the two separate solids</b> like in a "bag".
The two solids remain unconnected. The compound is just a set of shapes, no more.