It seems hard to find a definition for either of the terms. From skimming through datasheets that contain these terms, I get the impression that both refer to programmable components which control the final RF circuitry. But what exactly is the difference?
The difference, if there is one, is manufacturer specific. A baseband processor and a baseband controller often perform the same functions - that of controlling every aspect of the RF hardware.
Some manufacturers like to use "baseband processor" in order to indicate that their controller performs functionality you might find higher on a communications stack, such as message decoding. For instance a WiFi baseband controller might still need to be attached to a processor to implement a full WiFi link, whereas a baseband processor might handle more of the communications stack and may attach directly to another network interface, USB, etc.