Biomineralization processes in living organisms result in the formation of skeletal elements with complex ultrastructures. Although the formation pathways in sea urchin larvae are relatively well known, the interrelation between calcite, amorphous calcium carbonate (ACC), and intracrystalline organics in adult sea urchin biominerals is less clear. Here, we study this interplay in the spines and test plates of the Paracentrotus lividus sea urchins. Thermogravimetric analysis coupled with differential scanning calorimetry or mass spectrometry measurements, nuclear magnetic resonance technique, and high-resolution powder X-ray diffraction show that pristine spines and test plates are composed of Mg-rich calcite and comprise about 1.2 to 1.6 wt % organics, 10 wt % of anhydrous ACC and less than 0.2 wt % of water. Anhydrous ACC originates from incomplete crystallization of a precursor ACC phase during biomineralization and is associated with intracrystalline organics at the molecular level. Molecular interactions at organic/inorganic interfaces cause calcite lattice distortions of the tensile type. The latter are amplified during ACC crystallization and finally disappear after heat-assisted destruction of organic molecules. Converting the measured lattice distortions (strains) into internal stress components, we follow stress evolution upon annealing and find that complete crystallization of ACC leads to the isotropy of residual stresses in all investigated skeletal parts. These results allow us to speculate that organic macromolecules are preferentially attached to different crystallographic planes in the pristine test and spine samples.