Hi Assiouras,
it's quite simple: fdb is the file format of the CAESES4.x and older releases, while cdb is the current format of CAESES5.x. There is no backwards compatibility (you can open an fdb in CAESES5 and save it as cdb, but not the other way around), hence the different file type. In addition, anything with an additional "c" indicates a non-commercial license and therefore cannot be opened with a commercial license.
Best regards,
Heinrich