One pixel at 72 dpi is 1.3333 pixels at 96 dpi. Both are the same physical length expressed against different assumed screen densities, and the two numbers are a fossil of the old divide between Macintosh and Windows.
About the units
Neither figure describes any real display. Apple's original Macintosh used a 72 dpi convention so that one screen pixel corresponded to one typographic point, making WYSIWYG layout straightforward: a 12-point font occupied 12 pixels. Microsoft chose 96 dpi for Windows, reasoning that a typical monitor was viewed further away than a page and that text needed to be a third larger to be equally readable. The two conventions coexisted for two decades, and cross-platform documents came out a third larger or smaller depending on which assumption the software made.
The exact factor
The factor is exactly 96 ÷ 72 = 4/3. A 100-pixel image at 72 dpi is the same physical size as a 133-pixel image at 96 dpi. The legacy persists in image metadata: scanned material and older graphics are often tagged 72 dpi, and placing such an image in a layout program at its nominal size gives something a third too large. Modern practice sidesteps the issue by treating raster images as pixel dimensions and specifying display size explicitly, but the dpi tag is still there in the file.
Where you meet this conversion
Legacy asset conversion and cross-platform layout work. Image files inherited from older Mac workflows carry 72 dpi metadata that has to be reinterpreted. Web graphics have no meaningful dpi at all — the browser uses pixel dimensions — yet designers still export at 72 dpi from habit, which is harmless but explains why the number persists. Screenshot dimensions, icon specifications and PDF rasterisation all touch the same 4/3 relationship.