Hello, In addition to having different form factors, differences exist in I/O and connector layout. The Edge-V is largely self-contained, a single board, though an optional extension board, the M2X, is available to mount an M.2 NVMe SSD, also offers POE.
The Edge is a System on a Module(SoM). An optional base board is available for the Edge, called the Captain. The Edge mounts(docks) to the base board. The Captain adds many functions, M.2 NVMe SSD mount and I/O to the Edge.
A specification comparison chart for the Edge family is here.
The Khadas DIY case can work with the Edge-V(without M2X), albeit with a small modification, see here.
For the Edge, or at least Edge+Captain, the Khadas Kap Case is available, it includes a mount for the TS050 display+touchscreen. I do not have the TS050, I use the Kap Case to house the Edge+Captain, the display mount can be left off of the Kap.
For more detailed information on the Edge, Edge-V and accessories, see here.