Converting between Old Navy and Gap trips people up because the two brands are cut differently. Old Navy runs large thanks to generous vanity sizing, while Gap runs a little large. Gap generally runs smaller than Old Navy, so you'll often need to size up when switching from Old Navy. The converter above corrects for this automatically by reading the body-measurement range behind each size rather than matching the letter on the tag.
As a quick guide: a size S in Old Navy converts to about a S in Gap, a M lands around a M, and a L is roughly a L. When your measurement falls near a boundary the tool flags it as a between-sizes case — worth checking the garment's own measurements before you order.