To go a little bit further than the semantic question regarding DEM/DTM/DSM, I'd like to know if there is a free (of charges and use) DTM datasets? And what about resolution?
As far as I know,only DSM are available to public for free.
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For a list of sources, see also here: http://grass.osgeo.org/wiki/Global_datasets
If you are in the UK there is the Ordnance Survey Land-Form PANORAMA dataset that is available as part of OS OpenData. It is available as a DTM or as contours. The DTM is designed for use at a scale of 1:50,000.
For more information, use the link below:
Unsure of your location, but you may want to try the USGS if you're in the US. I think resolution is variable based on location, but you may find something of use here: