Of course "fax" is a shortening of "facsimile", so early
machines were often called "facsimile machines" and people referred
to sending a fax as "sending a facsimile". A couple of other names,
are telefax and telecopier. Today, a common kind of machine is a
multi-function machine that is a copier/scanner/printer/fax. These
are called multi-function machines, multi-function printers, or
all-in-one's.