In the United States, generally a DTM refers to DEM model that includes breaklines to better model the elevation. Here is a URL that gives a fuller explanation of the differences between DSM, DEM, and DTM: http://gisgeography.com/dem-dsm-dtm-differences/
ISO TC211 based information (relevant to the topic):
Terms:
1. Digital item - structured digital object [asset, work, service, data or information] with a standard representation, identification and metadata framework [ISO 19132:2007(E)]
2. Surface - 2-dimensional geometric primitive, locally representing a continuous image of a region of a plane [ISO 19107:2003(E)]
3. Terrain - not defined by ISO TC211.
4. Elevation - not defined by ISO TC211.
5. Model - abstraction of some aspect of reality [ISO 19118:2011(E)]
Abbreviations:
1. Digital Elevation Model (DEM) - dataset of elevation values that are assigned algorithmically to 2-dimensional coordinates [ISO/TS 19101-2:2008(E)].
2. Digital Surface Model (DSM) - not defined by ISO TC211 (predictable based on terms).
3. Digital Terrain Model (DTM) - not defined by ISO TC211.
I would agree with Franks description in the main and have recommended it as such. I believe in some American literature in particular, DEM is used as a generic term.
For a bit more information, but perhaps adding further to the confusion, if using LiDAR and following a data classification procedure ie ground, above ground, buildings etc., you can use the subtraction of the DSM from the DTM to create a DEM if you were to only look at the 'ground' classified surfaces, or conversely, you could subtract the DTM from the DSM to make canopy height models (CHM) if you were only interested in looking at vegetation for instance.
I may have gone a bit off topic here - but hope this adds to your understanding of what these terms are and how the data and terms can be used. From my reading though, I would certainly say that there are regional differences in these terms and how they are used.
DEM ( Digital Elevation Model) usually refers to representation of the earth surface without features such as streams, breaklines and ridges. DEM is commonly used in the USA.
DTM (Digital Terrain Model) is simply a representation of the surface of the earth.
DSM ( Digital Surface Model) is a representation of terrain surface including objects such as trees and buildings.
Some agencies simply prefer to use DTED (Digital Terrain Elevation Model) for better clarity.
I think that these definition are different as we reprensent some applications like DEM for all digital repreentation of the land surface issued from remote sensing or photograpmmetry for example. The reference will be a mathematical surface as an WGS ellipsoid . Also the DTM term is reference to "geoid", an equipotential surface of the gravity field and the refrerence surface of the altimetric height coordinates.
Digital Elevation Models (DEMs) are a type of raster GIS layer. In a DEM, each cell of raster GIS layer has a value corresponding to its elevation at regularly spaced intervals).
A digital terrain model (DTM) can be described as a 3–D representation of a terrain surface consisting of X, Y, Z coordinates stored in digital form. It includes not only heights and elevations but other geographical elements and natural features such as rivers, ridge lines, etc.