The primary difference between spectra obtained through a prism and a grating lies in their resolution and free spectral range. Diffraction gratings provide a higher resolution compared to prisms, allowing for more precise spectral analysis. However, prisms have a greater free spectral range, enabling them to separate wavelengths more effectively over a wider range. This distinction is crucial for applications in spectroscopy and optical analysis. Understanding these differences can enhance the selection of optical instruments for specific scientific needs.