You only ever get one of the two Fossils, either Claw or Root, but not both. The best way to obtain the opposite Fossil Pokémon is probably to breed yours and put the baby on the GTS, requesting the other Pokémon. Many people eager to complete the Pokédex will jump at the chance to get their missing Fossil Pokémon.
Other Fossil Pokémon
You can obtain the all of the other Fossil Pokémon in ORAS via Rock Smash, although some are version-exclusive.
Alpha Sapphire — Cover Fossil, Helix Fossil, Plume Fossil
Omega Ruby — Armour Fossil, Dome Fossil, Skull Fossil
Both Versions — Old Amber