Andreas' Topic on piece sets has got me thinking about how to group shape/sticker modifications. I will limit my discussion to shape modifications of the 3x3x3 cube, since they are the most common, but feel free to add to my definition.

Thinking on how a modification affects solution method, I propose the following classifications:

Class I Modification - Aesthetic
An aesthetic modification would affect the way a puzzle looks but not the solution. Therefore, turning functions the same and the solution can be accomplished with the same method.

3x3x3 examples:
Bump Cube (Mirror Blocks)
Truncated Cuboctahedron

Class II Modification - Abstracted
An abstracted modification encompasses the bulk of shape mods due to it's wide range. Mechanically, the puzzle functions the same, but the solution imposed new requirements. Pieces that previously did not previously require orientation do, pieces have fewer or more permutation requirements.

3x3x3 examples:
Mastermorphix
Fisher Cube

Class III Modification - Obstructed
An obstructed modification imposed new mechanical impediments that did not previously exist, making previous solution methods no longer viable.

3x3x3 example:
Bandage Cube

Let me know what you think!

Hrrm.
On this level of abstractness your scheme okay and complete.

The problems arise when one wants to precisely classify how the puzzle was "abstracted" or "obstructed".
If things like the Fischer Cube or the Octagon were to be covered we would need set notations.
A scheme for classifying obstructed puzzles is (again; CFF #79 anyone?) on its way. Sadly only the true bandaged cubes can be covered yet and it is almost non-understandable for humans. The only alterantive I know is not precise enough.