Honestly, I'd be pretty perplexed to hear that. I would guess – and I stress that this is an attempt to make sense out of something that doesn't make a lot of sense – that "pass your message" means "record a message after the tone, and we'll listen to it and transcribe it, and give the transcription to Department X", while "forward your message" means "we'll forward your call right on to Department X's own answering machine, and you can leave a message where they'll hear it for themselves, without our being in the loop".
Are you sure that you heard it say forward your message and not forward your call? Because forwarding a call means connecting in real time to another phone number; forwarding a message means alerting someone (by any medium) that they have a voice mail recording waiting for them to hear, or transcribing it or summarizing it for them.
Alternatively, might option 2 have been for Department Y? In which case, "pass" and "forward" might just be being used as synonyms, as I'd expect.