Most of all models are resolved in some sort of projected space. It depends on the model (e.g GFS uses an inflated cube, the ICON global from dwd is projected on to an icosahedron, IFS just moves most of the calcs to a spectral space instead of point-grid, and many regional/meso scale domains use a conic projection). Also by and large it’s easier to assume the earth is spherical and then nudge any differences in datum to Mach your crs.

Most often, final global models are output on to an orthogonal (plate-caree) lat/lon grid. Data at the poles (singularity) is always a bit fidly