To put it simply, looks.
Fresh film is, well, fresh. It has been produced in the last 3 years and expires the current year of shooting or later. Expired film was produced in the last 15-30 years, and has long been expired. The obvious difference is that one is expired and one isn't, but what do they look like?
Fresh has fine grain, and proper ISO sensitivity. Fresh film looks like regular film. For example, Kodak Gold 200. Kodak Gold has medium level contrast and typically has a good amount of exposure latitude.
Expired film does not have this same exposure latitude or "give" to the film. Instead, the grain is much more coarse. This however, gives off an interesting look that can't be replicated digitally.