Can iCloud password and Mail password be different if they are the same ID?

I have an idea that might work. Normally, no... that would be one PW for everything. But if you turn on two-factor authentication security for your AppleID, it allows you to setup application specific passwords so third party apps like Fantastical and others can access iCloud information.

I don't see it mentioned either way in the documentation, but I'm wondering if you could create an application specific PW and use it like you described. Worth a try.

https://support.apple.com/en-us/HT204397