This is why I said *usually*. DTM basically means DEM in most places, but in the US it refers to something different (i.e., what you're describing), see page 48 of the
USGS Lidar Base Specification document, specifically:
>digital terrain model (DTM) See two different definitions below:
>• In some countries, DTMs are synonymous with DEMs, representing the bare-earth ter-
rain with uniformly spaced z-values, as in a raster.
>• As used in the United States, a “DTM” is a vector dataset composed of 3D breaklines
and irregularly spaced 3D mass points, typically created through stereo photogram-
metry, that characterize the shape of the bare-earth terrain. Breaklines more precisely
delineate linear features whose shape and location would otherwise be lost. A DTM
is not a surface model and its component elements are discrete and not continuous; a
TIN or DEM surface must be derived from the DTM. Surfaces derived from DTMs can
represent distinctive terrain features much better than those generated solely from grid-
ded elevation measurements. A lidar dataset combined with ancillary breaklines is also
considered a DTM