What's the difference between compound paths and compound shapes in Illustrator?
Terminology in Illustrator can be irritating. Those two constructs sound related, but are not the same at all. Especially in the English speaking world they can be conveniently abbreviated as »compounds« and then nobody can tell anymore what people are talking about.
Compound paths and (to a lesser extent) compound shapes are both not only Illustrator objects, but you can find them in other software too. Mostly vector software, but not limited to it.
A vector software package that doesn’t have compound paths shouldn’t be allowed to be called a vector software in my opinion. In a compound path you combine paths that are then treated as one path. The paths can be separate, or (partly) overlap.
You use the fill rules (or winding rules) to define how a compound path acts at the overlaps. What’s important is the look at the layers panel:
Each compound path is only one entry in the layers panel, although they are nondestructive and can still be released. This is important for making clipping masks that consist of more than one path. You need a compound path for that.
Compound shapes are a more complex kind of object. They can interact in different ways, using the 4 top buttons in the pathfinder panel - the shape modes:
In the layers panel compound shapes are more complex as well since they are container objects that have the original paths as content. This also allows you to assign different effects to the single paths inside the compound shape (only certain effects unfortunately). As you can see in my example there are appearances applied (dark grey target symbol in the layers panel).
This is not all. In compound shapes you can create complex hierarchies and add more paths to already existing compound shapes by using different shapes modes. And you can use symbol instances as well as live text in a compound shape. All of this allows you to create complex shapes that are editable until a very late stage of production.
Comppound shapes can also help fight a common (and very nasty) problem with disappearing shapes that you can encounter while using consecutive pathfinder operations. Please watch the video to see how that works:
And since compound shapes also work in Photoshop this allows you to export PSD files out of Illustrator that contain shape layers. Of course for the shape layer export you can’t use live effects, text or symbols in your compound path, because Photoshop does not understand that part.
To summarize: compound paths are a more general vector graphic concept, while compound shapes (although supported in some other applications) are rather a proprietary Illustrator concept for live editing. Something like a precursor for »live paint« and related features.