Vertical and horizontal resolution of DEM

"Resolution" refers to what can be resolved, meaning, what can differentiated from that which it is not. Typically we're talking about some frequency, or, in other words, some periodicity or repeating interval. With a DEM, we have horizontal resolution, which is the spatial frequency at which samples are taken or modeled - the pixel size in x and y directions, those usually being equal and thus pixels being usually square. We also have vertical resolution in a DEM, which refers to how frequently the DEM can record a difference in elevation. Often, in my experience, this is in integer meters, or feet. So vertical resolution is often higher (i.e., more fine) than horizontal resolution. There is also temporal resolution, though most DEMs are single snap-shots in time, and temporal resolution starts to be measureable when we've got DEM series through time.