Boss and Ibanez seemed to define this difference with their pedals. The Boss OD-1 and Ibanez TS-9 Tube screamer "overdrives" are a smoother, less harsh sound than the DS-1 and SD-9 distortions.
The distortion pedals add more crunchy, gritty sound, whereas the overdrives add more smoothness and not as much distorted crunch. An MXR "distortion plus" is the definitive distortion pedal from the 1970s.
"Fuzz" seems to be an easier term to agree on a definition for.
Pretty much everyone involved agrees that fuzz is a harder, harsher, and
buzzier distortion than overdrive, and usually considered harder and harsher
than "distortion" by itself. There is no real boundary on all this -
it's just which words you want to use, no strict definitions.