Is serverless the new unhosted?

Regarding the term "Serverless", the community is still converging on what that means. I think there's definite overlap with Unhosted, but where I see the terms separate is with regard to how much concern is regarded for backend infrastructure. For example, with AWS Lambda, I can focus precisely on business/secret logic around with no regard to physical or virtual hardware and I get monitoring out of the box. In contrast, with Unhosted, I may or may not use something like Lambda to feed my client-side application into the browser, and then in my application, it proxies data through a unified API a la remoteStorage that talks to some data providers (ie: Google Drive, Dropbox, etc). What do you think?