Extrude

The most common use is to extrude a selected face or faces.  It can also be used to extrude edges.

The options are extrusion distance, number of segments (second image below), rotation angle (third image below) and scale (right image below).  

If Grouping Type is set to No Grouping, a face will be extruded from each of the selected faces see the second image in the bottom row which is an extrude of the first image in the bottom row.

The third image in the bottom row shows an extrude of 4 faces with the Area Weighted Normal option.  This option creates a single normal by area weighting all normals of the selected faces. The fourth image shows the Each Vertex Selected Faces which computes a different normal for each vertex based on the selected faces.  The fifth image shows Each Vertex All Faces, which computes a different normal for each vertex using all faces adjacent to that vertex not just the selected ones.

Available in Face and Edge mode.


Extend

Extend takes selected open edges and extends them along the edges of the adjacent faces.



Hinge

Extrudes a face or faces hinging from the specified edge. After initializing the tool, you can set the number of segments and affect the angle of the final face. You must select the hinge edge to initialize the tool.  

The top left image shows a hinge with the selected edge on the face.  The top right image below shows a hinge with an edge not on the face.  The bottom left image shows a 90 degree hinge with 5 segments.  The bottom right image shows a hinge with multiple faces.

Available from Face mode.



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