> what makes an email different from a web page, other than that it has been sent to you?
I think it's to do with perceived ownership of the environment in which the information is consumed.
Your website... feel free to style, brand, make pretty or ugly. You can make the experience consistent within your realm.
My inbox... I get to control my workflows, how I consume things, in which order, etc. I choose to make the experience consistent within my realm.
That holds fairly well as a definition for why I prefer chat clients that grant me the ability to make all messages consistent, and that do not allow the sender to dictate terms. It also holds up with things like Netflix, it's their realm they can knock themselves out on their design.
It does seem to be whether the environment it is presented is "yours" or "mine".