The difference, by the numbers
Both have grenadine. Only the Chapman has orange soda, lemon-lime soda, alcohol-free aromatic bitters, cucumber and lime juice; only the Shirley Temple has lemon juice and ginger ale. In parts, a Chapman is 1 orange soda and 1 lemon-lime soda; a Shirley Temple is 1 grenadine, 1¼ lemon and 22 ginger ale. By volume, the Chapman is 94% mixer and juice and 6% syrup and sugar; the Shirley Temple is 90% mixer and juice, 6% citrus and 4% syrup and sugar. That makes them close cousins on the ratio map.
They are about equally strong in the glass (both 0.0% ABV), and they hold about the same alcohol (0.00 standard drinks each). The Chapman has more calories (about 209 against 86) and more sugar (47.6 g against 19.9 g). Both are built and served in a highball.