The difference between the phosphorous cycle and carbon cycle lies in the fact that

The correct option is: the phosphorous cycle does not include a gaseous phase but the carbon cycle does.

To understand why this is the case, we can break down the nature of biogeochemical cycles into two main categories: gaseous cycles and sedimentary cycles.
Both carbon and phosphorus are essential elements for life, but they circulate through the biosphere in fundamentally different ways.

The Carbon Cycle (A Gaseous Cycle):
Carbon is a key component of organic molecules. The carbon cycle is classified as a gaseous cycle because its primary reservoir is the atmosphere, where carbon exists in a gaseous form as:
$C{O}_2$
(carbon dioxide). Processes such as photosynthesis, respiration, combustion, and decomposition continuously exchange carbon between the atmosphere, oceans, and living organisms. Because carbon moves through the air, it has a prominent gaseous phase.

The Phosphorus Cycle (A Sedimentary Cycle):
Phosphorus is crucial for forming nucleic acids (DNA and RNA), ATP, and cell membranes. Unlike carbon, the phosphorus cycle is a sedimentary cycle. The primary reservoir of phosphorus is not the atmosphere, but rather rock formations and ocean sediments. Phosphorus is released through the weathering of rocks and is absorbed by plants from the soil in the form of phosphate ions:
$P{O}_4^{3-}$
Under normal earth surface conditions of temperature and pressure, phosphorus and its compounds do not form stable gases, meaning there is no significant gaseous phase in its global cycle.

Conclusion:
Therefore, the key distinction between the two cycles is that the carbon cycle relies heavily on an atmospheric, gaseous phase (carbon dioxide), whereas the phosphorus cycle is localized primarily in terrestrial and aquatic ecosystems, completely lacking a gaseous atmospheric component.