I've seen in several astrophysical articles the following projection used to transform (spherical) equatorial coordinates $(\alpha,\delta)$ of a dataset, to rectangular $(x,y)$ coordinates:
$$ x = (\alpha - \alpha_0) * \cos(\delta)\\ y = (\delta - \delta_0) $$
where $(\alpha_0,\delta_0)$ are the coordinates of the center of the dataset. The equations look very similar to the Cylindrical Equidistant Projection, but not quite.
Can the projection above be considered a cylindrical projection?
It is shifted Sinusoidal Projection.