I am not sure that is a great distinction. A server is traditionally serving some resource, usually to multiple people. The idea behind 'home cloud' is to host 'slice' of a server yourself. Something that used to be hard because of the cost of hardware, making hosting only a few 'sessions' expensive.

Of course hardware hasn't been expensive for probably a decade or more. Today it is almost entirely a software problem. Or more precisely how to create independent quality software when many developers are employed by large corporations and no one wants to pay for development. I am not sure much is happening on that front.