It is not uncommon to find in the LiDAR/forestry literature the acronyms DTM and DEM being used as synonyms.
However, according to Behrendt (2012; paragraph 6 on page 15), there is a difference between them:
DTM: bare-earth representation with irregular spaces between points (non-raster).
DEM: gridded raster representation of the DTM.
Still according to Beherendt (2012; paragraph 4, on page 15):
DSM as a raster. This represents the first echo the laser received for each laser pulse sent out, and represents the tops of buildings, trees, and other objects, or the ground, if unobstructed.
And to complete, a CHM (Canopy Height Model) or nDSM (normalized Digital Surface Model) is the DEM subtracted from the DSM, i.e., CHM = DSM - DEM.
Behrendt, R. Introduction to LiDAR and forestry, part 1: a powerful new 3D tool for resource managers. The Forestry Source, p. 14-15, set. 2012. link.