It’s called an ambulance, but it isn’t like a medical ambulance, with all kinds of emergency equipment inside. It’s really just a van, because all it has to do is transport a dead body, and it’s usually painted white or maybe black, with no lettering on the sides. It couldn’t really be called a “van”, because on such occasions one should be respectful towards the deceased, so it’s given the more-tasteful description of “ambulance”. A “hearse” carries the deceased in a coffin from the funeral home/parlour/undertaker’s to the place where the funeral is to be held.

I would assume an ambulance would do the initial heavy lifting if this is for storytelling purposes.

hearst ?

A hearse or an ambulance. If the funeral home transports the body, they use a hearse.

A hearse is a funeral vehicle, a conveyance for the casket from e.g. a church to a cemetery, a similar burial site, or a crematorium. In the funeral trade, they are often called funeral coaches.