How is being a caregiver for the mentally ill be different than helping someone with another condition?

Quite different. Mentally ill people may be very challenging to work with in that they exhibit symptoms that may be hard to handle, such uncontrollable emotions, unusual behaviors - anger (excessive), panic attacks, violent behaviors, hallucinations, delusions etc. A caregiver for such patients must be ready to intervene on an emergent basis to refer such patients for acute care. There may some safety risk involv.