Diatoms, a highly successful group of photosynthetic algae, contribute to a quarter of global primary production. Many species are motile, despite having no appendages and a completely rigid cell body. Cells move to seek out nutrients, locate mating partners, and undergo vertical migration. To explore the natural diversity of diatom motility, we perform a comparative study across five common biofilm-forming species. Combining morphological measurements with high-resolution cell tracking, we establish how gliding movements relate to the morphology of the raphe -- a specialised slit in the cell wall responsible for motility generation. Our detailed analyses reveal that cells exhibit a rich but species-dependent phenotype, switching stochastically between four stereotyped motility states. We model this behaviour and use stochastic simulations to predict how heterogeneity in microscale navigation patterns leads to differences in long-time diffusivity and dispersal. In a representative species, we extend these findings to quantify diatom gliding in complex, naturalistic 3D environments, suggesting that cells may exploit these distinct motility signatures to achieve niche segregation in nature.