A CD is definitely not "physically the same" as a single-layer DVD. However, I've read that if you burn a DVD-compatible file system onto a CD, a few DVD players and most computer DVD player software will interpret it as a DVD.
Videohelp.com calls this non-standard "DVD format on a CD" a miniDVD or cDVD. However, Wikipedia points out miniDVD is also used to mean an 8-cm DVD disc.
Searching for miniDVD or cDVD might help you find how to properly burn this format if you want to play around with it. Just be careful the results you find are talking about the "DVD format on a CD" and not the 8-cm DVD disc.
For example, here's a videohelp.com post that suggests you'll need to use DVD authoring software to make a DVD image file (or directory structure), then use a burning program to burn the image (or directory structure in UDF/ISO9660 mode) onto the CD.