The rate of change in the relative amount of active and passive carbon (AC and PC) due to the land management practices (cropping systems combined with tillage) may vary with soil types depending on their level of chemical and/or physical protection from the decomposition but has rarely been directly measured. We have quantified the C storage potentiality of different soil types, namely old alluvial Inceptisol of Malda and recent alluvial Entisol of Coochbehar in West Bengal (subtropical eastern India) under the influence of different cropping systems (rice-maize: RM and rice-wheat: RW) and tillage practices (zero-tillage: ZT and conventional tillage: CT). The key objective was to demonstrate the short-term impact of conservation agriculture (CA) on soil C dynamics over the conventional practice. Research revealed that after short-term CA, total organic carbon (TOC), AC, PC, and total nitrogen (TN) showed significant (p < 0.05) improvement under the RM cropping system over the RW. The highest TOC content under the RM cropping system was recorded in the sites of Malda over the Coochbehar sites. The ZT significantly (p < 0.05) enhanced the TOC in the upper layers (0–5 and 5–10 cm) and the CT showed improvements in the lower depths (10–20 cm). We observed some irregular variations in the interactions of the cropping system and tillage with respect to different sites. However, the ZT performed better in improving C fractions under RM and RW as compared to CT. The TOC and TN stocks were maximum in the lower depth which was evident in both soil types. The TOC linearly regressed on TN accounted for 94.2% variability (R2 = 0.942) of the C accumulation in soil and vice-versa. The PC was in a significant relationship with TN (R2 = 0.943), but AC was moderately regressed (R2 = 0.851). Lower stratification ratio values in Coochbehar soils (sandy loam in texture) indicated higher profile distribution of AC and PC in the soil profile; while in the Inceptisol, accumulation of the C fractions on the soil surface due to heavy texture resulted in the higher stratification values. The novelty of this study is that old alluvial Inceptisol showed a comparatively greater amount of AC and PC storage capability in comparison with the new alluvial Entisol. Conclusively, our study demonstrated that the adoption of conservation agriculture (CA practice/ZT) in cropping systems with higher C biomass input would significantly enhance the AC and PC fractions; however, the amount of storage is highly governed by the soil type and climatic factors.