Why photo counts might differ between Photos in iOS, macOS, and iCloud.com

Computers are supposed to be good at counting, right? So why do the numbers sometimes not add up for photos? Macworld reader Jeffrey asks a question that’s similar to ones asked by others:
The photo count between my Mac and my iPhone are not the same. I use iTunes syncing along with My Photo Stream to keep the devices identical. Something has gone amiss. I don’t have any idea how to troubleshoot the image counts since iTunes is supposed to be syncing the images. How might I determine