All servers are hosts, but not all hosts are servers.
Any device that has established a connection to a network qualifies as a host, whereas only hosts that accept connections from other devices (clients) qualify as servers.
The use of the word server in computing comes from queueing theory, where it dates to the mid 20th century, being notably used in Kendall (1953) (along with "service"), the paper that introduced Kendall's notation. In earlier papers, such as the Erlang (1909), more concrete terms such as "operators" are used.
In computing, "server" dates at least to RFC 5 (1969), one of the earliest documents describing ARPANET (the predecessor of Internet), and is contrasted with "user", distinguishing two types of host: "server-host" and "user-host". The use of "serving" also dates to early documents, such as RFC 4, contrasting "serving-host" with "using-host".