When considering resolution, there are a few important distinctions to make. Due to the nature of the printing process, resolution horizontally (aka. the x-y plane) and vertically (z direction) are different and determined by separate effects. These are then also different from the finest detail possible on a printer.
Printing resolution in the x-y plane is limited by the minimum distance the nozzle or laser of a printer can move (with the exception of DLP where resolution depends on pixel size), while in the z direction, it’s limited by layer thickness. The smaller each of these values, the better the resolution. Resolution will determine the accuracy of the edges of a printed object, allowing for finer increments in, for example, a curved surface.
In the diagram below, shapes b)-e) are trying to recreate the shape in a) with varying resolution. Starting from b), the print is limited in print quality by the x-y and z resolution, hence, doubling resolution in the x-y plane or z has no effect on the overall accuracy of the print as accuracy will be limited by the other unchanged resolution. Only by doubling resolution in x-y and z will improve accuracy.
Therefore, it can be seen high resolution in both the x-y plane and z direction are needed to produce accurate and smooth prints. However, smaller layer thickness (so better z resolution) isn’t necessarily always better. Thinner layers also means more layers and, therefore, more chance for a defect or printing error to occur with little improvement to the smoothness of a surface. This is clear if comparing a sloped surface with increasing z resolution and a vertical surface with increasing z resolution. Thinner layers in the vertical surface will have no improvement in the print while the slope would see improvement (assuming z resolution is the limiting factor for overall resolution). Layer thickness can also affect properties in adverse ways. The exact effect that changing layer thickness has on properties such as strength can be quite complex and won’t be discussed here.
Finest detail (also known as minimum feature size) is a measure of the smallest section of an object able to be made by the printer. The smaller the finest detail, the better. Finest detail is generally limited by either nozzle diameter or laser spot size. Details smaller than these values cannot be printed as the printer is physically unable to produce lines that small. However, practically, other factors may effect this. For example, due to the heat of melted plastic from FDM printers, thin sections can fail due to softening from the heat.
Typically, print quality is most limited by z resolution and the minimum feature size (as x-y resolution is usually high for printers). For best quality, careful selection of layer thickness and small minimum feature size is needed.