The FV-1 is the IC that does all the work. It is the DSP in this case. It's a 28-pin SMD IC.
The EEPROM is where the effects are stored. It can hold up to eight different effects.
It is an 8-pin through-hole IC that looks similar to an opamp. You can socket it and swap it for different effects.
There are two multi-purpose FV-1 PCBs here, the Arachnid and the Pythagoras. They are basically identical functionally, the only difference being that the Arachnid uses an 8-position rotary switch and can use all eight slots of the EEPROM. The Pythagoras uses a 3-position toggle switch and can only access the first three slots of the EEPROM.
You're exactly right, you can swap out the EEPROM and have a different set of effects with either PCB. Any effect in the "EEPROM Builder" will work on either PCB.
The Octagon, Spatialist, and Module 8 projects all include the same Arachnid PCB with a different EEPROM.
The Daydream, D3lay, ThreeVerb, and Unison projects all include the Pythagoras PCB with a different EEPROM.
Any of the EEPROMs will work in either PCB, but as mentioned above, the Pythagoras PCB can only access the first three algorithms on the EEPROM.
The Hydra, DMD-2, Organ Donor, and Deflector all use a specialized PCB. The EEPROMs for these projects will not function as expected in any other PCB, and any other EEPROM will not function as expected in their PCB.
The Leprechaun is the oddball of the group, it doesn't use an EEPROM. Instead it uses one of the internal programs included in the FV-1.
This one also requires a specialized PCB.
The HAARP EEPROM will technically work in the Arachnid PCB but since it doesn't have a "Direction" toggle switch one of the knobs would behave as the direction control. (Below Noon = Down, Past Noon = Up)