Not really. "Cloud" refers to a software abstraction that tries to hide the existence of actual hardware namely to remove dependence on the availability of any specific hardware component (like, as in, being able to transparently move to another physical machine without the user ever knowing). It is clearly a software term. I can't go down to my local Walmart and buy a "Cloud". Amazon won't ship a "Cloud" to my place. There is nothing "hard" implied by the word as used in this context. I'll grant you that it more or less maintains some kind of "virtual" hardware concept. Perhaps that is what you mean?

There is no hardware association with "serverless". It refers to a pattern for developing a certain breed of applications that resemble servers, but without the server. "Server" is definitively a software term as used here. A server is an application that listens for requests from a client, typically on a network port if we are to dive into implementation territory, but could be something else like a unix domain socket. Much like CGI of yore, these "serverless" applications shed the server, relying on the runtime environment to fill in the missing pieces.