Context. The composition of rocky planets is strongly driven by the primordial materials in the protoplanetary disk, which can be inferred from the abundances of the host star. Understanding this compositional link is crucial for characterizing exoplanets. Aims. We aim to investigate the relationship between the compositions of low-mass planets and their host stars. Methods. We determined the primordial compositions of host stars using high-precision present-day stellar abundances and stellar evolutionary models. These primordial abundances were then input into a stoichiometric model to estimate the composition of planet-building blocks. Additionally, we employed a three-component planetary interior model (core, mantle, and water in different phases) to estimate planetary compositions based only on their radius and mass. Results. We find that although stellar abundances vary over time, relevant abundance ratios such as Fe/Mg remain relatively constant during the main sequence evolution for low temperature stars. A strong correlation is found between the iron-to-silicate mass fraction of protoplanetary disks and planets, while no significant correlation was observed for water mass fractions. The Fe/Mg ratio varies significantly between planets and their stars, indicating substantial disk-driven compositional diversity, and this ratio also correlates with planetary radius. Conclusions. While stellar abundances, as a proxy of the composition of protoplanetary disk, provide a baseline for planetary composition, significant deviations arise due to complex disk processes, challenging the assumption of a direct, one-to-one elemental relationship between stars and their planets.