In the instructions for "Modify a Compound Shape," it says to "click a different shape mode button." This would be more helpful if it said "opt- or alt-click a different shape mode button."
Without the opt or alt modifier, clicking the other shape modes will just produce an error ("The filter produced no results. Please select two intersecting paths").
If you make a compound path (by, for example, draw a circle inside a square, select both, press Ctrl-8), that path is a single object (a path), and not a "compound shape."
If you place a circle inside a square (with the circle on top), and then Alt-Click the "minus front" Shape Mode in the Pathfinder panel, you'll create a compound shape.
The main difference is that the compound shape is dynamic. You can sub-select the circle and move it around, thereby altering the resulting compound shape object.
I'm not sure what you're trying to do, but remember that you can select the sub-shapes of a compound shape with the Direct Selection tool (white arrow). Clicking with the white arrow will select path segments or anchor points, but Alt-Clicking will select whole sub-shapes.
I hope this helps...
Thank you for the quick response! This is very helpful. I'm still a bit confused on how they all work and which to use to accomplish what I need to do, but I can fumble along and make it work for my needs until I grasp the concepts! One question ... is the command "divide objects below" doing the same thing, but via the menu instead of the pathfinder palette or is it an entirely different operation?
Divide Objects Below is similar to one of the Shape Builder tools, although I can't recall off the top of my head which one it emulates. It leaves a Compound Shape, which can get very complicated if you're dividing several objects at once. I haven't run into a situation where this command is especially useful, but there is probably a use-case where it's a perfect match.
Basically, this command uses the top object, which must be selected, to cut through ALL the objects below it. The top object is then deleted, and the objects below, sliced up as if by the cookie cutter, remain as a compound shape. At first, the sliced object(s) may not be obvious: internal paths usually end up with no stroke applied. But if you select it, you'll see it's called "Compound Shape" and the newly modified paths will be visible. (If only some paths are visible, make sure View / Hide Edges isn't checked (Ctrl-H).)
You can then use the Direct Select (white) arrow to reposition portions of the Compound Shape, but again, if it's very complex, there may be several overlapping internal paths which result in confusing visibility of holes. I recommend searching the main help file for this command ("Divide Objects Below") and then referring to the section on the Pathfinder panel. It's also important to understand how compound paths result in holes.
In most situations, Pathfinder provides more useful tools.
Note also that Pathfinder tools are also available as live effects in the Appearance Panel. These are all permutations of combining objects with each other, and some of them do more than one thing. They're quite powerful, and I recommend getting familiar with them by experimenting a lot.
I've summarized all the Pathfinder panel tools here:
(It's a work in progress...)
Using the divide tool in pathfinder automatically groups the result. This means your compund shape and a shape matching the hole in your compound shape (as a result of using divide) are grouped. The hole is not "visible" because it is the exact same shape as the hole. Ungroup and you can move the compound shape and reveal the "hole-shape". Making two paths into a compound path makes the two into one object. Pathfinder have no problem dealing with compound paths ;-)