Umm, here's the deal.
A ROM is a full system (operating system) that needs to have nothing installed already on your phone to work. There is no compatibility with the existing ROM on your phone - only the requirements of having access to a particular type of Recovery in order to install the ROM. It will remove your old ROM currently on your phone, so no compatibility required.
A theme is applied over a currently installed ROM on your phone, and these will require compatibility - some themes are nearly universal, but some are ROM version specific.
A themed-ROM is a hybrid of the above two - it takes (usually) a stock ROM and applies a particular theme on top of it so you only flash one thing and get your chosen ROM with your chosen them applied already. These work the same as regular ROMs - since it is the full ROM, you flash and go. It wipes the previous ROM out of the way, so no compatibility required.
HTH