@βj

A milling machine is often called a mill by machinists. The term miller also used to be common (19th and early 20th centuries), although it is typically not used today in reference to modern machines. (The term "miller" is one that people today are still familiar with from historical usage, but they generally don't use it anymore unless they are referring to machines built during the term's heyday, which is similar to the way that people today treat terms such as "motor car", "horseless carriage", or "phonograph".)

The distinction, when one is made, is that a machining center is a mill with features that pre-CNC mills never had, especially an automatic tool changer (ATC) that includes a tool magazine (carousel), and sometimes an automatic pallet changer (APC). 

@Bj