A store is where carbon is held; a transfer is the process moving it. Carbon dioxide in air is an atmospheric store; living biomass is biospheric; dissolved carbon is hydrospheric; carbonate rock and fossil carbon are geospheric stores.
Photosynthesis transfers carbon from atmospheric CO₂ into biomass. Respiration and decomposition return carbon to the atmosphere or water. Combustion rapidly transfers carbon in fuels/biomass to atmospheric CO₂. Oceans exchange carbon with the atmosphere, and geological processes act over much longer timescales.
The carbon cycle is a network, not a simple circle. Different pathways operate at different rates. Carbon atoms are rearranged into different substances; they are not created by combustion.