Famous means widely known, with no judgement attached. Infamous means well known for something bad — notorious. It is not a stronger version of famous, which is the common misuse: "the infamous chef" says the chef is disgraced, not celebrated.
The core difference
Not degrees of the same thing. One is neutral, the other condemnatory.
- famous — widely known: a famous painting.
- infamous — known for something bad: the infamous forgery.
Why the misuse spreads
The in- prefix usually negates — so infamous looks like it should mean "not famous", and when that plainly is not the meaning, people reach for "very famous" instead. In fact it comes from Latin infamis, of ill repute, where in- negates fama in the sense of good name.
The noun
Infamy means the state of being notorious for wrongdoing. Roosevelt's "a date which will live in infamy" uses it exactly — not a date that will be well remembered, but one remembered for something shameful.
