Compression schemes like PNG and ZIP try to find repeating patterns in image data (of even more generic: repeating data patterns in any file). Searching for these patterns really can take a while, especially when the files are relatively large, offering many possible patterns, resulting in more compression rates, and smaller files.

But if the speed of saving (compressing) the file is crucial, then you can opt for letting the software just try a few quick and easy patterns and be happy with it. The file is probably larger, albeit that in cases of simple web imagery it really doesn't make a big difference...

Note: this is only valid for compressing the file, not for decompressing.

Oorspronkelijk geplaatst op Quora: When saving a .PNG file using Adobe Photoshop, what's the difference between the "None / Fast" and "Smallest / Slow" compression options?"