The difference
Lemon-lime soda and bitters in both, here made with alcohol-free bitters. Lemon, Lime and Bitters adds fresh lime juice; the Rock Shandy cuts the soda with plain soda water instead, so it is less sweet and lighter.
By the numbers
The Lemon, Lime and Bitters uses lime juice where the Rock Shandy uses soda water; both have lemon-lime soda and alcohol-free aromatic bitters. In parts, a Lemon, Lime and Bitters is 1 lime and 10 lemon-lime soda; a Rock Shandy is 1 lemon-lime soda and 1 soda. By volume, the Lemon, Lime and Bitters is 91% mixer and juice and 9% citrus; the Rock Shandy is 100% mixer and juice.
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 Lemon, Lime and Bitters has more calories (about 68 against 51) and more sugar (16.5 g against 13.0 g). Both are built and served in a highball.