Digital elevation model (DEM) : Generic term covering digital topographic data in all its various forms as well as the method for interpreting implicitly of the elevations between observations (Maune et al., 2001).
Digital terrain model (DTM) : DTM is a synonym of bare-earth DEM (Maune et al., 2001). Florinsky 1998, defined DTMs as digital representations of variables relating to a topographic surface, namely: digital elevation models (DEMs), digital models of gradient (G), aspect (A), horizontal (Kh) and vertical (Kv) land surface curvatures as well as other topographic attributes.
Digital surface model (DSM) : Model depicting elevations of the top of reflective surfaces, such as buildings and vegetation (Maune et al., 2001).
The digital terrain model (DTM Digital Terrain Model), unlike the DEM is obtained by the interpolation of contour lines. It is often confused with the DEM and the main difference between the two models lies in the fact that the DEM takes into account all persistent objects on the ground (vegetation, buildings, and other artifacts), while the DTM shows the development of the geodesic surface. The difference between the two models is most evident in urban areas where the prevailing high-rise buildings, for example the island of Manhattan or that of Hong Kong.
Let me clarify this with a simple example for better understanding:
DSM-DTM= Height of the objects standing in the surface of the earth that are either natural like trees canopy or man made like buildings, towers, electric poles etc.
A DSM expresses digital representation of the elevation of all objects within an area of interest, A DTM on the other hand, is a digital rendition of the ground elevation of a surface of interest. The DEM is a is digital cartographic/geographic data in raster form. The terrain elevations for ground positions are sampled at regularly spaced horizontal intervals.
DEM and DTM are the most used concepts. As mentioned above, the DTM is mostly a topographic terminology for elevation of the Earth, while DEM takes into account the real landscape situation that includes heights of buildings, constructions, forest etc. The DSM is a synonym of the DTM, that is digital surface (or terrain) model.
A DEM is a bared-earth raster which non-ground (man-made) features such as roads and building aren’t included in it. DEM is useful for hydrological modeling, surface analyzing, and soil mapping.
Whereas DTM is a 3D model of visualizing surface elevation data; its structure is based on the TIN which is vector data. A DTM reinforces a DEM by including man-made features of the bare-earth terrain.
DEM - (Digital Elevation Model) a raster - regular matrix - of points with X, Y, and elevation of the bared terrain.
DTM - (Digital Terrain Model) DEM + irregular lines (ridges, riverbeds, cliffs) + irregular points (summits and bassins).
DSM - (Digital Surface Model) DTM + elevations of all structures that exist above the terrain (trees, buildings, ...). Many times a shortcut is produced which is DEM + the mentioned structures.