ipc-d-356b format
IPC-D-356 is a standardized netlist format. It is not a Gerber format. It contains information about the test points and net connections on a board. It was intended to provide a standard set of information for bare board testing. You can find the table of contents for the standard at:
http://www.ipc.org/TOC/IPC-D-356B.pdf
ODB++ is a board fabrication data set developed by Valor. It contains everything about the board - the cad data, netlist, fabrication data, etc. Unfortunately, Valor hasn't done a very good job of sharing the data format completely with the rest of the world. The result is that often times an ODB++ file produced by a PCB program can't be properly read by other CAM or CAD software. Valor has a free reader that can display a board that was saved as ODB++, but you can't use the display for anything except viewing. It also has trouble reading a file if there is even the slightest difference from the Valor "standard". You can see more about the format by going to
http://www.valor.com/ , then select "Solutions", "ODB++ Data Exchange".
Don't believe all the hype on that page about how great the format is supposed to be - as I said above, the format has a lot of inconsistency from vendor to vendor.
Of the two file types you asked about, ODB++ is the only one that contains enough information to completely reconstruct the PCB. IPC-D-356 won't tell you anything about the trace widths, component orientations, special board features, etc. - it is strictly for testing net connectivity.