An astigmatic lens has two principal axes with different focal lengths, so for the lens shown, rays in the vertical plane focus more strongly than those in the horizontal plane. In a lens with astigmatism, light from a point source will produce a blur, rather than a sharp focus. Field curvature appears because the object and image distances are measured from the lens' center. All of the points on that sphere will focus on another sphere of radius v , which is also centered on the lens' geometric center. Distortion appears when the magnification of a lens depends on how far the object point is from the optical axis.
Barrel distortion occurs when the central parts of an image are magnified more than the outer parts.
Most microscope samples aren't curved, however. The effect of field curvature for flat samples makes it impossible to perfectly focus both the center and the edge of the field simultaneously. If you focus on what's in the center, parts of the sample off axis will be out of focus and vice versa. How big an effect field curvature has depends on the angular field of view. The working distance is just the object distance for the objective lens.