A320 IDG and GEN
 

Is the IDG and and Engine generator the same? If they are the same, then why are there separate PBs on the overhead ELEC panel? If they have different purposes, they what are they?

Not correct. The GEN pb when selected OFF removes the generator field voltage thereby removing the output from the generator due no field voltage, no generation, no output.

Not being Airbus, but IDG's are usually connected and driven by the HP (N2) system (N3 on some RR types) and the guarded flight deck switch will physically cause a solenoid to bring about a drive disconnect; re-connection is only possible when the engine is static on the ground.
When the IDG looses drive or under-speeds, the associated generator control unit, GCU, will take it off line by de-exciting it and opening its GLC.
On the B727 there was a field control switch/contactor, but the FE could also adjust the frequency and parallel generators, that is old techy.

The idg pb disconnects PHYSICALLY and Irreversibly the IDG from the shafts.
Engine generator just shuts the field and line contractor opens.
Dsc24-20-overhead panel dedcription.

Strictly speaking, it's not "irreversible", just not reversible from the flight deck.

Thank you for your replies