Classifying cracks in walls, floors, beams and columns is not as simple as that chart implies. Identifying a crack visually as vertical, horizontal, diagonal or stair-step is acceptable and understandable by most people. Stresses such as tension, compression, shear, thermal, torsional or a combination of them will likely have contributed to 95% of the cracks most inspectors see. The $64,000 question clients want to know is can it be repaired or prevented from getting worst. Answering these two questions is like taking puzzle pieces from several different puzzles and giving them to someone who never saw the completed puzzles before. You have to look at the puzzle pieces you have and try to put them together and hope you can develop a picture you recognize. Something as simple as a shrinkage crack in a concrete foundation may be the result of a combination of factors. Factors such as concrete mix design, environmental factors like temperature and wind combined with reinforcement placement and early form removal. Months later poor soil compaction under the footing can turn that shrinkage crack in to a wider variable width settlement crack. You can quickly see the complexity of diagnosing cracks can lead to misidentification and potential liability issues.
IMO home inspectors should describe cracks based on the visual characteristics and recommend further evaluation, on the more serious cracks. The structural engineer or geological engineer can help answer the questions is it stable and does it require repair. The answers may require more investigation to get more puzzle pieces. Once the engineer based on past experience doing similar investigations combined with their technical skills is satisfied enough evidence has been collected then and only then should experience contractors be called in to do the repair work, if needed.
That’s what I do.