In the case of soxs_disp_solution the output dispersion map hosts the coefficients ($c_{ij}$) to two polynomials that describe the global dispersion solution for the entire detector frame:
$$
X = \sum\limits_{ij} c_{ij} \times n^i \times \lambda^j \\
$$
$$
Y = \sum\limits_{ij} c_{ij} \times n^i \times \lambda^j \\
$$
soxs_spatial_solution, building from this dispersion solution, provides global dispersion and spatial solution. The dispersion map output by this recipe hosts the coefficients ($c_{ijk}$) to two polynomials (note now the inclusion of slit position):
$$
X = \sum\limits_{ijk} c_{ijk} \times n^i \times \lambda^j \times s^k \\
$$
$$
Y = \sum\limits_{ijk} c_{ijk} \times n^i \times \lambda^j \times s^k \\
$$